Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"The global Cauchy problem for the Euler–Riesz equations","authors":"Young-Pil Choi ,&nbsp;Jinwook Jung ,&nbsp;Yoonjung Lee","doi":"10.1016/j.na.2024.113724","DOIUrl":"10.1016/j.na.2024.113724","url":null,"abstract":"<div><div>We completely resolve the global Cauchy problem for the multi-dimensional Euler–Riesz equations, where the interaction forcing is given by <span><math><mrow><mo>∇</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mi>σ</mi><mo>/</mo><mn>2</mn></mrow></msup><mi>ρ</mi></mrow></math></span> for some <span><math><mrow><mi>σ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. We construct the global-in-time unique solution to the Euler–Riesz system in a <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span> Sobolev space under a smallness assumption on the initial density and a <em>dispersive</em> spectral condition on the initial velocity. Moreover, we investigate the algebraic time decay of convergences for the constructed solutions. Our results cover the both attractive and repulsive cases as well as the whole regime <span><math><mrow><mi>σ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"253 ","pages":"Article 113724"},"PeriodicalIF":1.3,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long-time asymptotics of the damped nonlinear Klein–Gordon equation with a delta potential","authors":"Kenjiro Ishizuka","doi":"10.1016/j.na.2024.113732","DOIUrl":"10.1016/j.na.2024.113732","url":null,"abstract":"<div><div>We consider the damped nonlinear Klein–Gordon equation with a delta potential: <span><span><span><math><mrow><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>−</mo><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><mn>2</mn><mi>α</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>u</mi><mo>−</mo><mi>γ</mi><msub><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>u</mi><mo>−</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>∈</mo><mi>R</mi><mo>×</mo><mi>R</mi><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>γ</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> denotes the Dirac delta with the mass at the origin. When <span><math><mrow><mi>γ</mi><mo>=</mo><mn>0</mn></mrow></math></span>, Côte et al. (2021) proved that any global solution either converges to 0 or to the sum of <span><math><mrow><mi>K</mi><mo>≥</mo><mn>1</mn></mrow></math></span> decoupled solitary waves which have alternative signs. In this paper, we first prove that any global solution either converges to 0 or to the sum of <span><math><mrow><mi>K</mi><mo>≥</mo><mn>1</mn></mrow></math></span> decoupled solitary waves. We then construct a single solitary wave solution that moves away from the origin when <span><math><mrow><mi>γ</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span> and construct an even 2-solitary wave solution when <span><math><mrow><mi>γ</mi><mo>≤</mo><mo>−</mo><mn>2</mn></mrow></math></span>. Last we give single solitary wave solutions and even 2-solitary wave solutions an upper bound for the distance between the origin and the solitary wave.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"253 ","pages":"Article 113732"},"PeriodicalIF":1.3,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Doubly-nonlinear evolution equations of rate-independent type with irreversibility and energy balance law","authors":"Kotaro Sato","doi":"10.1016/j.na.2024.113716","DOIUrl":"10.1016/j.na.2024.113716","url":null,"abstract":"<div><div>In this paper, the global-in-time <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-solvability of the initial–boundary value problem for differential inclusions of doubly-nonlinear type is proved. This problem arises from fracture mechanics, and it is not covered by general existence theories due to the degeneracy and singularity of a dissipation potential along with the nonlinearity of elliptic terms. The existence of solutions is proved based on a minimizing movement scheme, which also plays a crucial role for deriving qualitative properties and asymptotic behaviors of strong solutions. Moreover, the solutions to the initial–boundary value problem comply with three properties intrinsic to brittle fracture: <em>complete irreversibility</em>, <em>unilateral equilibrium of an energy</em> and <em>an energy balance law</em>, which cannot generally be realized in dissipative systems. Furthermore, long-time dynamics of strong solutions are revealed, i.e., each stationary limit of the global-in-time solutions is characterized as a solution to the stationary problem.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"253 ","pages":"Article 113716"},"PeriodicalIF":1.3,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak solutions for steady, fully inhomogeneous generalized Navier-Stokes equations","authors":"Julius Jeßberger,&nbsp;Michael Růžička","doi":"10.1016/j.na.2024.113715","DOIUrl":"10.1016/j.na.2024.113715","url":null,"abstract":"<div><div>We consider the question of existence of weak solutions for the fully inhomogeneous, stationary generalized Navier–Stokes equations for homogeneous, shear-thinning fluids. For a shear rate exponent <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math></span>, previous results require either smallness of the norm or vanishing of the normal component of the boundary data. In this work, combining previous methods, we propose a new, more general smallness condition.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"253 ","pages":"Article 113715"},"PeriodicalIF":1.3,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-posedness of a network transport model","authors":"Michiel Bertsch ,&nbsp;Emilia Cozzolino ,&nbsp;Veronica Tora","doi":"10.1016/j.na.2024.113714","DOIUrl":"10.1016/j.na.2024.113714","url":null,"abstract":"<div><div>We prove existence and uniqueness of solutions of a model for the progression of soluble and insoluble toxic Tau proteins on a graph of nerve cells in an Alzheimer brain. The model was recently introduced to deal with the existence of two timescales in Alzheimer’s disease, a fast one for most of the involved physical and chemical mechanisms and a much slower one for the evolution of the disease. Considering the physical and chemical mechanisms as instantaneous, one obtains a quasi-static model in the slow timescale. The model combines an active transport mechanism of soluble Tau on the edges of the graph with the dynamics of Tau at the nodes.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"253 ","pages":"Article 113714"},"PeriodicalIF":1.3,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lie groups of real analytic diffeomorphisms are L1-regular","authors":"Helge Glöckner","doi":"10.1016/j.na.2024.113690","DOIUrl":"10.1016/j.na.2024.113690","url":null,"abstract":"<div><div>Let <span><math><mi>M</mi></math></span> be a compact, real analytic manifold and <span><math><mrow><mi>G</mi><mo>≔</mo><msup><mrow><mo>Diff</mo></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> be the Lie group of all real-analytic diffeomorphisms <span><math><mrow><mi>γ</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></mrow></math></span>, which is modelled on the locally convex space <span><math><mrow><mi>g</mi><mo>≔</mo><msup><mrow><mi>Γ</mi></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>T</mi><mi>M</mi><mo>)</mo></mrow></mrow></math></span> of real-analytic vector fields on <span><math><mi>M</mi></math></span>. Let <span><math><mrow><mo>AC</mo><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>,</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> be the Lie group of all absolutely continuous functions <span><math><mrow><mi>η</mi><mo>:</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>→</mo><mi>G</mi></mrow></math></span>. We study flows of time-dependent real-analytic vector fields on <span><math><mi>M</mi></math></span> which are <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> in time, and their dependence on the time-dependent vector field. Notably, we show that the Lie group <span><math><mrow><msup><mrow><mo>Diff</mo></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-regular in the sense that each <span><math><mrow><mrow><mo>[</mo><mi>γ</mi><mo>]</mo></mrow><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>,</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span> has an evolution <span><math><mrow><mo>Evol</mo><mrow><mo>(</mo><mrow><mo>[</mo><mi>γ</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>∈</mo><mo>AC</mo><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>,</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> which depends smoothly on <span><math><mrow><mo>[</mo><mi>γ</mi><mo>]</mo></mrow></math></span>. As tools for the proof, we develop new results concerning <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-regularity of infinite-dimensional Lie groups, and new results concerning the continuity and complex analyticity of non-linear mappings on locally convex direct limits.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"252 ","pages":"Article 113690"},"PeriodicalIF":1.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142702102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the endpoint case","authors":"Bing Li ,&nbsp;Cui Ning","doi":"10.1016/j.na.2024.113713","DOIUrl":"10.1016/j.na.2024.113713","url":null,"abstract":"<div><div>We consider the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrödinger equation <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><mi>i</mi><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn><mi>σ</mi></mrow></msup><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>σ</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span>. The equation has a two-parameter family of solitary wave solutions of the form <span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>ω</mi><mo>,</mo><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>ω</mi><mi>t</mi><mo>+</mo><mi>i</mi><mfrac><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>c</mi><mi>t</mi><mo>)</mo></mrow><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>2</mn><mi>σ</mi><mo>+</mo><mn>2</mn></mrow></mfrac><msubsup><mrow><mo>∫</mo></mrow><mrow><mo>−</mo><mi>∞</mi></mrow><mrow><mi>x</mi><mo>−</mo><mi>c</mi><mi>t</mi></mrow></msubsup><msubsup><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi><mo>,</mo><mi>c</mi></mrow><mrow><mn>2</mn><mi>σ</mi></mrow></msubsup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mi>d</mi><mi>y</mi></mrow></msup><msub><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi><mo>,</mo><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>c</mi><mi>t</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span></span></span>The stability theory in the frequency region of <span><math><mrow><mrow><mo>|</mo><mi>c</mi><mo>|</mo></mrow><mo>&lt;</mo><mn>2</mn><msqrt><mrow><mi>ω</mi></mrow></msqrt></mrow></math></span> was thoroughly studied previously. In this paper, we prove the instability of the solitary wave solutions in the endpoint case <span><math><mrow><mi>c</mi><mo>=</mo><mn>2</mn><msqrt><mrow><mi>ω</mi></mrow></msqrt></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"252 ","pages":"Article 113713"},"PeriodicalIF":1.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142702103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Examples of tangent cones of non-collapsed Ricci limit spaces","authors":"Philipp Reiser","doi":"10.1016/j.na.2024.113699","DOIUrl":"10.1016/j.na.2024.113699","url":null,"abstract":"<div><div>We give new examples of manifolds that appear as cross sections of tangent cones of non-collapsed Ricci limit spaces. It was shown by Colding–Naber that the homeomorphism types of the tangent cones of a fixed point of such a space do not need to be unique. In fact, they constructed an example in dimension 5 where two different homeomorphism types appear at the same point. In this note, we extend this result and construct limit spaces in all dimensions at least 5 where any finite collection of manifolds that admit <em>core metrics</em>, a type of metric introduced by Perelman and Burdick to study Riemannian metrics of positive Ricci curvature on connected sums, can appear as cross sections of tangent cones of the same point.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"252 ","pages":"Article 113699"},"PeriodicalIF":1.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A useful subdifferential in the Calculus of Variations","authors":"Piernicola Bettiol ,&nbsp;Giuseppe De Marco ,&nbsp;Carlo Mariconda","doi":"10.1016/j.na.2024.113697","DOIUrl":"10.1016/j.na.2024.113697","url":null,"abstract":"<div><div>Consider the basic problem in the Calculus of Variations of minimizing an energy functional depending on absolutely continuous functions Under suitable assumptions on the Lagrangian, a well-known result establishes that the minimizers satisfy the Du Bois-Reymond equation. Recent work (cf. Bettiol and Mariconda, 2020 <span><span>[1]</span></span>, 2023; Mariconda, 2023 <span><span>[2]</span></span>, 2021, 2024) highlights not only that a Du Bois-Reymond condition for minimizers can be broadened to cover the case of nonsmooth extended valued Lagrangians, but also that a particular subdifferential (associated with the generalized Du Bois-Reymond condition) plays an important role in the approximation of the energy via its values along Lispchitz functions, no matter minimizers exist. A crucial point is establishing boundedness properties of this subdifferential, based on weak local boundedness properties of the Lagrangian. This is the main objective of this paper. Our approach is based on a refined analysis of the metric that can be employed to evaluate the distance from the complementary of the effective domain of the reference Lagrangian. As an application of our findings we show how it is possible to deduce the non-occurrence of the Lavrentiev phenomenon, providing a new general result.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"252 ","pages":"Article 113697"},"PeriodicalIF":1.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence versus finite time blowup dichotomy for the dispersion managed NLS","authors":"Mi-Ran Choi ,&nbsp;Younghun Hong ,&nbsp;Young-Ran Lee","doi":"10.1016/j.na.2024.113696","DOIUrl":"10.1016/j.na.2024.113696","url":null,"abstract":"<div><div>We consider the Gabitov–Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>av</mi></mrow></msub><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mrow><mo>(</mo><mrow><msup><mrow><mrow><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>r</mi><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msup><mi>u</mi></mrow><mo>)</mo></mrow><mi>d</mi><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span></span></span>and prove the global existence versus finite time blowup dichotomy for the mass-supercritical cases, that is, <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>9</mn></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113696"},"PeriodicalIF":1.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}