Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"A family of explicit minimizers for interaction energies","authors":"Ruiwen Shu","doi":"10.1016/j.na.2025.113900","DOIUrl":"10.1016/j.na.2025.113900","url":null,"abstract":"<div><div>In this paper we consider the minimizers of the interaction energies with the power-law interaction potentials <span><math><mrow><mi>W</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>a</mi></mrow></msup></mrow><mrow><mi>a</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>b</mi></mrow></msup></mrow><mrow><mi>b</mi></mrow></mfrac></mrow></math></span> in <span><math><mi>d</mi></math></span> dimensions. For odd <span><math><mi>d</mi></math></span> with <span><math><mrow><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>−</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span> and even <span><math><mi>d</mi></math></span> with <span><math><mrow><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>−</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span>, we give the explicit formula for the unique energy minimizer up to translation. For the odd dimensions, the key observation is that successive Laplacian of the Euler–Lagrange condition gives a local partial differential equation for the minimizer. For the even dimensions <span><math><mi>d</mi></math></span>, the minimizer is given as the projection and rescaling of the previously constructed minimizer in dimension <span><math><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math></span> via a new lemma on dimension reduction.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113900"},"PeriodicalIF":1.3,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633185","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":"Threshold dynamics approximation schemes for anisotropic mean curvature flows with a forcing term","authors":"Bohdan Bulanyi,&nbsp;Berardo Ruffini","doi":"10.1016/j.na.2025.113899","DOIUrl":"10.1016/j.na.2025.113899","url":null,"abstract":"<div><div>We establish the convergence of threshold dynamics-type approximation schemes to propagating fronts evolving according to an anisotropic mean curvature motion in the presence of a forcing term depending on both time and position, thus generalizing the consistency result obtained in Ishii, Pires and Souganidis (1999) by extending the results obtained in Caffarelli and Souganidis (2010) for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> to anisotropic kernels and in the presence of a driving force. The limit geometric evolution is of a variational type and can be approximated, at a large scale, by eikonal-type equations modeling dislocations dynamics. We prove that it preserves convexity under suitable convexity assumptions on the forcing term and that convex evolutions of compact sets are unique. If the initial set is bounded and sufficiently large, and the driving force is constant, then the corresponding generalized front propagation is asymptotically similar to the Wulff shape.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113899"},"PeriodicalIF":1.3,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633186","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":"A note on entire large solutions to semilinear elliptic systems of competitive type","authors":"Alan V. Lair","doi":"10.1016/j.na.2025.113903","DOIUrl":"10.1016/j.na.2025.113903","url":null,"abstract":"<div><div>We consider the elliptic system <span><math><mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>p</mi><mrow><mo>(</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>v</mi></mrow><mrow><mi>b</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>Δ</mi><mi>v</mi><mo>=</mo><mi>q</mi><mrow><mo>(</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mi>c</mi></mrow></msup><msup><mrow><mi>v</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> (<span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span>) where <span><math><mi>a</mi></math></span>, <span><math><mi>b</mi></math></span>, <span><math><mi>c</mi></math></span>, <span><math><mi>d</mi></math></span> are positive constants with <span><math><mrow><mo>min</mo><mrow><mo>{</mo><mi>a</mi><mo>,</mo><mi>d</mi><mo>}</mo></mrow><mo>&gt;</mo><mn>1</mn></mrow></math></span>, and the functions <span><math><mi>p</mi></math></span> and <span><math><mi>q</mi></math></span> are positive and continuous. We establish conditions on <span><math><mi>p</mi></math></span> and <span><math><mi>q</mi></math></span>, along with the exponents <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mrow></math></span>, which ensure the existence of a positive entire solution satisfying <span><math><mrow><msub><mrow><mo>lim</mo></mrow><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>→</mo><mi>∞</mi></mrow></msub><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>lim</mo></mrow><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>→</mo><mi>∞</mi></mrow></msub><mi>v</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113903"},"PeriodicalIF":1.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631329","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":"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}