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Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the β-plane
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-24 DOI: 10.1016/j.na.2025.113794
Aseel Farhat , Anuj Kumar , Vincent R. Martinez
{"title":"Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the β-plane","authors":"Aseel Farhat ,&nbsp;Anuj Kumar ,&nbsp;Vincent R. Martinez","doi":"10.1016/j.na.2025.113794","DOIUrl":"10.1016/j.na.2025.113794","url":null,"abstract":"<div><div>This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier–Stokes equation for viscous, incompressible fluids on the <span><math><mi>β</mi></math></span>-plane. Previous results in this setting by Al-Jaboori and Wirosoetisno (2011) had proved that the global attractor collapses to a single point that depends only the latitudinal coordinate, i.e., <em>zonal flow</em>, when the rotation is sufficiently fast. However, an explicit quantification of the complexity of the global attractor in terms of <span><math><mi>β</mi></math></span> had remained open. In this paper, such estimates are established which are valid across a wide regime of rotation rates and are consistent with the dynamically degenerate regime previously identified. Additionally, a decomposition of solutions is established detailing the asymptotic behavior of the solutions in the limit of large rotation.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113794"},"PeriodicalIF":1.3,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682854","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}
引用次数: 0
The L1-relaxed area of the graph of the vortex map: Optimal lower bound
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-22 DOI: 10.1016/j.na.2025.113803
Giovanni Bellettini , Alaa Elshorbagy , Riccardo Scala
{"title":"The L1-relaxed area of the graph of the vortex map: Optimal lower bound","authors":"Giovanni Bellettini ,&nbsp;Alaa Elshorbagy ,&nbsp;Riccardo Scala","doi":"10.1016/j.na.2025.113803","DOIUrl":"10.1016/j.na.2025.113803","url":null,"abstract":"<div><div>We prove a lower bound for the value of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-relaxed area of the graph of the map <span><math><mrow><mi>u</mi><mo>:</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>l</mi></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><mi>x</mi><mo>/</mo><mo>|</mo><mi>x</mi><mo>|</mo></mrow></math></span>, <span><math><mrow><mi>x</mi><mo>≠</mo><mn>0</mn></mrow></math></span>, for all values of the radius <span><math><mrow><mi>l</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In the computation of the singular part of the relaxed area, for <span><math><mi>l</mi></math></span> in a certain range, in particular <span><math><mi>l</mi></math></span> not too large, a nonparametric Plateau-type problem with partial free boundary has to be solved. Our lower bound turns out to be optimal, in view of an upper bound proven in a companion paper.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113803"},"PeriodicalIF":1.3,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682853","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}
引用次数: 0
Bifurcation of double eigenvalues for Aharonov–Bohm operators with a moving pole
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-19 DOI: 10.1016/j.na.2025.113798
Laura Abatangelo , Veronica Felli
{"title":"Bifurcation of double eigenvalues for Aharonov–Bohm operators with a moving pole","authors":"Laura Abatangelo ,&nbsp;Veronica Felli","doi":"10.1016/j.na.2025.113798","DOIUrl":"10.1016/j.na.2025.113798","url":null,"abstract":"<div><div>We study double eigenvalues of Aharonov–Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues when the potential’s circulation is a fixed half-integer number and the operator’s pole is moving on straight lines in a neighborhood of the origin. We prove that bifurcation occurs if the pole is moving along straight lines in a certain number of cones with positive measure. More precise information is given for symmetric domains; in particular, in the special case of the disk, any eigenvalue is double if the pole is located at the center, but there exists a whole neighborhood where it bifurcates into two distinct branches.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113798"},"PeriodicalIF":1.3,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643666","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}
引用次数: 0
Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-13 DOI: 10.1016/j.na.2025.113796
Prashanta Garain
{"title":"Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations","authors":"Prashanta Garain","doi":"10.1016/j.na.2025.113796","DOIUrl":"10.1016/j.na.2025.113796","url":null,"abstract":"<div><div>This article is divided into two parts. In the first part, we examine the Brezis–Oswald problem involving a mixed anisotropic and nonlocal <span><math><mi>p</mi></math></span>-Laplace operator. We establish results on existence, uniqueness, boundedness, and the strong maximum principle. Additionally, for certain mixed anisotropic and nonlocal <span><math><mi>p</mi></math></span>-Laplace equations, we prove a Sturmian comparison theorem, establish comparison and nonexistence results, derive a weighted Hardy-type inequality, and analyze a system of singular mixed anisotropic and nonlocal <span><math><mi>p</mi></math></span>-Laplace equations. A key component of our approach is the use of the Picone identity, which we adapt from the local and nonlocal cases. In the second part of the article, we focus on regularity estimates. In the elliptic setting, we establish a weak Harnack inequality and semicontinuity results. We also consider a class of doubly nonlinear mixed anisotropic and nonlocal parabolic equations, proving semicontinuity results and analyzing the pointwise behavior of solutions. These results rely on appropriate energy estimates, De Giorgi-type lemmas, and positivity expansions. Finally, we derive various energy estimates, which may be of independent interest.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113796"},"PeriodicalIF":1.3,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611687","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}
引用次数: 0
On the existence of a second positive solution to mixed local-nonlocal concave–convex critical problems
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-13 DOI: 10.1016/j.na.2025.113795
Stefano Biagi , Eugenio Vecchi
{"title":"On the existence of a second positive solution to mixed local-nonlocal concave–convex critical problems","authors":"Stefano Biagi ,&nbsp;Eugenio Vecchi","doi":"10.1016/j.na.2025.113795","DOIUrl":"10.1016/j.na.2025.113795","url":null,"abstract":"<div><div>We prove the existence of a second positive weak solution for mixed local-nonlocal critical semilinear elliptic problems with a sublinear perturbation in the spirit of Ambrosetti et al. (1994).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113795"},"PeriodicalIF":1.3,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611686","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}
引用次数: 0
Some rigidity results for charged initial data sets 带电初始数据集的一些刚度结果
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-01 DOI: 10.1016/j.na.2025.113780
Gregory J. Galloway , Abraão Mendes
{"title":"Some rigidity results for charged initial data sets","authors":"Gregory J. Galloway ,&nbsp;Abraão Mendes","doi":"10.1016/j.na.2025.113780","DOIUrl":"10.1016/j.na.2025.113780","url":null,"abstract":"<div><div>In this note, we consider some initial data rigidity results concerning marginally outer trapped surfaces (MOTS). As is well known, MOTS play an important role in the theory of black holes and, at the same time, are interesting spacetime analogues of minimal surfaces in Riemannian geometry. The main results presented here expand upon earlier works by the authors, specifically addressing initial data sets incorporating charge.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113780"},"PeriodicalIF":1.3,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519275","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}
引用次数: 0
Nonexistence of global solutions to the Euler–Poisson–Darboux equation in Rn: Subcritical case
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-26 DOI: 10.1016/j.na.2025.113781
Mengting Fan , Ning-An Lai , Hiroyuki Takamura
{"title":"Nonexistence of global solutions to the Euler–Poisson–Darboux equation in Rn: Subcritical case","authors":"Mengting Fan ,&nbsp;Ning-An Lai ,&nbsp;Hiroyuki Takamura","doi":"10.1016/j.na.2025.113781","DOIUrl":"10.1016/j.na.2025.113781","url":null,"abstract":"<div><div>The singular Cauchy problem for the semilinear Euler–Poisson–Darboux equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with power type nonlinearity is studied in this paper. We show that the blow up power is related to the Strauss exponent, which generalizes the blow up result from the regular semilinear wave equation with scale invariant damping to the corresponding singular problem, and hence give some affirmative answer partially to the open problem posed by D’Abbicco in a recent paper.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113781"},"PeriodicalIF":1.3,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509684","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}
引用次数: 0
Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-24 DOI: 10.1016/j.na.2025.113778
Masaki Kawamoto , Hayato Miyazaki
{"title":"Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials","authors":"Masaki Kawamoto ,&nbsp;Hayato Miyazaki","doi":"10.1016/j.na.2025.113778","DOIUrl":"10.1016/j.na.2025.113778","url":null,"abstract":"<div><div>This paper is concerned with nonlinear Schrödinger equations with a time-decaying harmonic potential. The nonlinearity is gauge-invariant of the long-range critical order. In Kawamoto and Muramatsu (2021) and Kawamoto (2021), it is proved that the equation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in the frameworks of both the final state problem and the initial value problem. Furthermore, a modified scattering operator has been established in the case without the potential in Hayashi and Naumkin (2006). In this paper, we construct a modified scattering operator for our equation by utilizing a generator of the Galilean transformation. Moreover, we remove a restriction for the coefficient of the potential which is required in Kawamoto (2021).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113778"},"PeriodicalIF":1.3,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474344","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}
引用次数: 0
Holder continuity and higher integrability of weak solutions to. double phase elliptic equations involving variable exponents and. critical growth
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-22 DOI: 10.1016/j.na.2025.113754
Dukman Ri, Sungil Kwon
{"title":"Holder continuity and higher integrability of weak solutions to. double phase elliptic equations involving variable exponents and. critical growth","authors":"Dukman Ri,&nbsp;Sungil Kwon","doi":"10.1016/j.na.2025.113754","DOIUrl":"10.1016/j.na.2025.113754","url":null,"abstract":"<div><div>We study a class of double phase elliptic equations with variable exponents and critical growth. In the present paper we establish the boundedness, Holder continuity and higher integrability of weak solutions for these equations. Our results partially generalize those obtained by Winkert and his collaborators (2023)</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113754"},"PeriodicalIF":1.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463542","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}
引用次数: 0
Interface logistic problems: Large diffusion and singular perturbation results
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-22 DOI: 10.1016/j.na.2025.113777
Pablo Álvarez-Caudevilla , Cristina Brändle , Mónica Molina-Becerra , Antonio Suárez
{"title":"Interface logistic problems: Large diffusion and singular perturbation results","authors":"Pablo Álvarez-Caudevilla ,&nbsp;Cristina Brändle ,&nbsp;Mónica Molina-Becerra ,&nbsp;Antonio Suárez","doi":"10.1016/j.na.2025.113777","DOIUrl":"10.1016/j.na.2025.113777","url":null,"abstract":"<div><div>In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled through such a membrane where we impose the so-called Kedem–Katchalsky boundary conditions. For this particular scenario we analyse the existence and uniqueness of positive solutions depending on the parameters involved in the system, obtaining interesting results where one can see for the first time the effect of the membrane under such boundary conditions. To do so, we first ascertain the asymptotic behaviour of several linear and nonlinear problems for which we include a diffusion coefficient and analyse the behaviour of the solutions when such a diffusion parameter goes to zero or infinity. Despite their own interest, since these asymptotic results have never been studied before, they will be crucial in analysing the existence and uniqueness for the main interface logistic problems under analysis. Finally, we apply such an asymptotic analysis to characterize the existence of solutions in terms of the growth rate of the populations, when both populations possess the same growth rate and, also, when they depend on different parameters.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113777"},"PeriodicalIF":1.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463543","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}
引用次数: 0
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