Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Uniqueness of solutions to the isotropic Lp Gaussian Minkowski problem","authors":"Jinrong Hu","doi":"10.1016/j.na.2025.113901","DOIUrl":"10.1016/j.na.2025.113901","url":null,"abstract":"<div><div>The uniqueness of solutions to the isotropic <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Gaussian Minkowski problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> is established when <span><math><mrow><mo>−</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>−</mo><mn>1</mn></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, without requiring the origin-centred assumption on convex bodies.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113901"},"PeriodicalIF":1.3,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144605020","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":"Global well-posedness to the three-dimensional compressible Navier–Stokes equations with anisotropic viscous stress tensor","authors":"Ying Wang ,&nbsp;Zhenhua Guo","doi":"10.1016/j.na.2025.113898","DOIUrl":"10.1016/j.na.2025.113898","url":null,"abstract":"<div><div>This paper addresses the Cauchy problem for the three-dimensional Navier–Stokes equations with anisotropic viscosity tensor. Under the condition that the initial energy is small enough, we establish the global existence and uniqueness of classical solutions and derive some decay rates. Notably, we extend the results for small energy solutions with isotropic viscous stress tensors originally established by Huang et al., (2012) to the anisotropic case.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113898"},"PeriodicalIF":1.3,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580084","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":"Local existence for the 2D Euler equations in a critical Sobolev space","authors":"Elaine Cozzi,&nbsp;Nicholas Harrison","doi":"10.1016/j.na.2025.113846","DOIUrl":"10.1016/j.na.2025.113846","url":null,"abstract":"<div><div>In the seminal work (Bourgain and Li, 2015), Bourgain and Li establish strong ill-posedness of the 2D incompressible Euler equations with vorticity in the critical Sobolev space <span><math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>. In this note, we establish short-time existence of solutions with vorticity in the critical space <span><math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. Under the additional assumption that the initial vorticity is Dini continuous, we prove that the <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>-regularity of vorticity persists for all time.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113846"},"PeriodicalIF":1.3,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580100","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":"Multiple cosmic strings in Chern–Simons–Higgs theory with gravity","authors":"Lei Cao,&nbsp;Shouxin Chen","doi":"10.1016/j.na.2025.113895","DOIUrl":"10.1016/j.na.2025.113895","url":null,"abstract":"<div><div>In this paper, we consider the self-dual equation arising from Abelian Chern–Simons–Higgs theory coupled to the Einstein equations over the plane <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a compact surface <span><math><mi>S</mi></math></span>. We prove the existence of symmetric topological solutions and non-topological solutions on the plane by using the fixed-point theorem and a shooting method, respectively. A necessary and sufficient condition related to the string number <span><math><mi>N</mi></math></span>, the Euler characteristic <span><math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mi>S</mi></math></span>, and the gravitational coupling factor <span><math><mi>G</mi></math></span> is given to show the existence of <span><math><mi>N</mi></math></span>-string solutions over a compact surface.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113895"},"PeriodicalIF":1.3,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580098","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":"Regularity of vectorial minimizers for non-uniformly elliptic anisotropic integrals","authors":"Pasquale Ambrosio ,&nbsp;Giovanni Cupini ,&nbsp;Elvira Mascolo","doi":"10.1016/j.na.2025.113897","DOIUrl":"10.1016/j.na.2025.113897","url":null,"abstract":"<div><div>We establish the local boundedness of the local minimizers <span><math><mrow><mi>u</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span> of non-uniformly elliptic integrals of the form <span><math><mrow><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>D</mi><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mi>d</mi><mi>x</mi></mrow></math></span>, where <span><math><mi>Ω</mi></math></span> is a bounded open subset of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> <span><math><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span> and the integrand satisfies anisotropic growth conditions of the type <span><span><span><math><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mo>≤</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>≤</mo><mi>μ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>ξ</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi></mrow></msup></mrow></mfenced></mrow></math></span></span></span>for some exponents <span><math><mrow><mi>q</mi><mo>≥</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> and with non-negative functions <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>μ</mi></mrow></math></span> fulfilling suitable summability assumptions. The main novelties here are the degenerate and anisotropic behavior of the integrand and the fact that we also address the case of vectorial minimizers (<span><math><mrow><mi>m</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>). Our proof is based on the celebrated Moser iteration technique and employs an embedding result for anisotropic Sobolev spaces.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113897"},"PeriodicalIF":1.3,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580099","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":"Remarks on the inviscid limit of weak solutions of the Navier–Stokes equations","authors":"Jiangyu Shuai,&nbsp;Ke Wang","doi":"10.1016/j.na.2025.113865","DOIUrl":"10.1016/j.na.2025.113865","url":null,"abstract":"<div><div>The paper analyzes the inviscid limit of weak solutions to the incompressible Navier–Stokes equations within physical boundaries. We establish a sufficient regularity condition that ensures the Navier–Stokes solutions exhibit global viscous dissipation. Moreover, we prove that as the viscous coefficient tends to zero, the weak solutions converge to those of the Euler equations. We assume that the weak solutions are uniformly bounded with respect to viscosity in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msup><mfenced><mrow><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>α</mi><mo>,</mo><mi>∞</mi></mrow></msubsup></mrow></mfenced></mrow></math></span> in the interior domain, and that certain mean integral conditions in the space–time region exhibit prescribed decay rates near the boundary.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113865"},"PeriodicalIF":1.3,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534929","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":"Combinatorial Ricci flow and Calabi flow for generalized hyperbolic circle packings","authors":"Yu Sun ,&nbsp;Kai Wang ,&nbsp;Xiaorui Yang ,&nbsp;Hao Yu","doi":"10.1016/j.na.2025.113894","DOIUrl":"10.1016/j.na.2025.113894","url":null,"abstract":"<div><div>In Hu et al. (2025), they studied a generalized hyperbolic circle packing (including circles, horocycles and hypercycles) with a total geodesic curvature on each generalized circle of this circle packing and a discrete Gaussian curvature on the center of each dual circle. In this paper, we introduce the combinatorial Ricci flow and combinatorial Calabi flow to find this type of generalized circle packings for a data including prescribed total geodesic curvatures of generalize circles and discrete Gaussian curvatures on centers of dual disks. We show that the solution to the combinatorial Ricci flow and combinatorial Calabi flow in the hyperbolic geometry with the given initial value exists for all the time and converges exponentially fast to a unique generalized circle packing metric.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113894"},"PeriodicalIF":1.3,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534424","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":"Nonlocal-to-local convergence of the Cahn–Hilliard equation with degenerate mobility and the Flory–Huggins potential","authors":"Charles Elbar ,&nbsp;Jakub Skrzeczkowski","doi":"10.1016/j.na.2025.113870","DOIUrl":"10.1016/j.na.2025.113870","url":null,"abstract":"<div><div>The Cahn–Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link interacting particle systems and continuous descriptions, has received much attention in recent years. In the recent article, we showed how to treat the case of degenerate mobility for the first time. Here, we discuss how to adapt the exploited tools to the case of the mobility <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>u</mi><mspace></mspace><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> as in the original works of Giacomin–Lebowitz and Elliot–Garcke. The main additional information is the boundedness of <span><math><mi>u</mi></math></span>, implied by the form of mobility, which allows handling the nonlinear terms. We also discuss the case of (mildly) singular kernels and a model of cell–cell adhesion with the same mobility. Another supplementary finding of our work is the energy and entropy inequalities for the nonlocal equation where we give a precise meaning to the dissipation terms despite the singularity of the potential.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113870"},"PeriodicalIF":1.3,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534930","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":"Lipschitz regularity of solutions to two-phase free boundary problems governed by a non-uniformly elliptic operator","authors":"Jefferson Abrantes Santos ,&nbsp;Sergio H. Monari Soares","doi":"10.1016/j.na.2025.113893","DOIUrl":"10.1016/j.na.2025.113893","url":null,"abstract":"<div><div>We will deal with a two-phase free boundary problem involving a degenerate non-uniformly elliptic operator with <span><math><mi>Φ</mi></math></span>-Laplacian type growth. We prove Lipschitz regularity for minimizers by controlling the negative phase density along the free boundary. It is also shown that the region where the local Lipschitz regularity fails is contained in the contact set between the positive and negative free boundaries and there the negative phase is cusp free. As an application, we prove Lipschitz regularity for a two-phase free boundary problem driven by the infinity Laplacian operator by studying the behavior of an <span><math><mi>ℓ</mi></math></span>-two-phase free boundary problem as <span><math><mrow><mi>ℓ</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113893"},"PeriodicalIF":1.3,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523097","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":"Infinite families of harmonic self-maps of ellipsoids in all dimensions","authors":"Volker Branding ,&nbsp;Anna Siffert","doi":"10.1016/j.na.2025.113874","DOIUrl":"10.1016/j.na.2025.113874","url":null,"abstract":"<div><div>We prove that for given <span><math><mrow><mi>k</mi><mo>∈</mo><mi>N</mi></mrow></math></span>, <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>∈</mo><mi>N</mi></mrow></math></span> and each <span><math><mrow><mi>a</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> with <span><span><span><math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&lt;</mo><mn>4</mn><mi>d</mi><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math></span></span></span>the ellipsoid <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>≔</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup><mspace></mspace><mo>|</mo><mspace></mspace><msup><mrow><mi>a</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><mo>…</mo><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> admits infinitely many harmonic self-maps.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113874"},"PeriodicalIF":1.3,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523098","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}