发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Analysis of PDEs最新文献

筛选
英文 中文
Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation 关于一维波方程导数半线性模型经典解存在性的说明
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06378
Takiko Sasaki, Hiroyuki Takamura
{"title":"Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation","authors":"Takiko Sasaki, Hiroyuki Takamura","doi":"arxiv-2409.06378","DOIUrl":"https://doi.org/arxiv-2409.06378","url":null,"abstract":"This note is a supplement with a new result to the review paper by Takamura\u0000[13] on nonlinear wave equations in one space dimension. We are focusing here\u0000to the long-time existence of classical solutions of semilinear wave equations\u0000in one space dimension, especially with derivative nonlinear terms of\u0000product-type. Our result is an extension of the single component case, but it\u0000is meaningful to provide models as possible as many to cover the optimality of\u0000the general theory. The proof is based on the classical iteration argument of\u0000the point-wise estimate of the solution.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global-in-time well-posedness for the two-dimensional incompressible Navier-Stokes equations with freely transported viscosity coefficient 具有自由传输粘度系数的二维不可压缩纳维-斯托克斯方程的全局时间内好拟性
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06517
Xian Liao, Rebekka Zimmermann
{"title":"Global-in-time well-posedness for the two-dimensional incompressible Navier-Stokes equations with freely transported viscosity coefficient","authors":"Xian Liao, Rebekka Zimmermann","doi":"arxiv-2409.06517","DOIUrl":"https://doi.org/arxiv-2409.06517","url":null,"abstract":"We establish the global-in-time well-posedness of the two-dimensional\u0000incompressible Navier-Stokes equations with freely transported viscosity\u0000coefficient, under a scaling-invariant smallness condition on the initial data.\u0000The viscosity coefficient is allowed to exhibit large jumps across\u0000$W^{2,2+epsilon}$-interfaces. The viscous stress tensor $mu Su$ is carefully analyzed. Specifically,\u0000$(R^perpotimes R):(mu Su)$, where $R$ denotes the Riesz operator, defines a\u0000``good unknown'' that satisfies time-weighted $H^1$-energy estimates. Combined\u0000with tangential regularity, this leads to the $W^{1,2+epsilon}$-regularity of\u0000another ``good unknown'', $(bar{tau}otimes n):(mu Su)$, where $bar{tau}$\u0000and $n$ denote the unit tangential and normal vectors of the interfaces,\u0000respectively. These results collectively provide a Lipschitz estimate for the\u0000velocity field, even in the presence of significant discontinuities in $mu$. As applications, we investigate the well-posedness of the Boussinesq\u0000equations without heat conduction and the density-dependent incompressible\u0000Navier-Stokes equations in two spatial dimensions.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding the convex hull of a set using the flow by minimal curvature with an obstacle. A game theoretical approach 利用有障碍物的最小曲率流寻找集合的凸面。博弈论方法
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06855
Irene Gonzálvez, Alfredo Miranda, Julio D. Rossi, Jorge Ruiz-Cases
{"title":"Finding the convex hull of a set using the flow by minimal curvature with an obstacle. A game theoretical approach","authors":"Irene Gonzálvez, Alfredo Miranda, Julio D. Rossi, Jorge Ruiz-Cases","doi":"arxiv-2409.06855","DOIUrl":"https://doi.org/arxiv-2409.06855","url":null,"abstract":"In this paper we look for the convex hull of a set using the geometric\u0000evolution by minimal curvature of a hypersurface that surrounds the set. To\u0000find the convex hull, we study the large time behavior of solutions to an\u0000obstacle problem for the level set formulation of the geometric flow driven by\u0000the minimum of the principal curvatures (that coincides with the mean curvature\u0000flow only in two dimensions). We prove that the superlevel set where the\u0000solution to this obstacle problem is positive converges as time goes to\u0000infinity to the convex hull of the obstacle. Our approach is based on a\u0000game-theoretic approximation for this geometric flow that is inspired by\u0000previous results for the mean curvature flow.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"137 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional 具有受控莫尔斯指数的帕莱-斯马尔序列的紧凑性，适用于刘维尔型函数
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06515
Francesco Malizia
{"title":"Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional","authors":"Francesco Malizia","doi":"arxiv-2409.06515","DOIUrl":"https://doi.org/arxiv-2409.06515","url":null,"abstract":"We prove that Palais-Smale sequences for Liouville type functionals on closed\u0000surfaces are precompact whenever they satisfy a bound on their Morse index. As\u0000a byproduct, we obtain a new proof of existence of solutions for Liouville type\u0000mean-field equations in a supercritical regime. Moreover, we also discuss an\u0000extension of this result to the case of singular Liouville equations.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized ground state solutions of Schrödinger-KdV system in $mathbb{R}^3$ 薛定谔-KdV 系统在 $mathbb{R}^3$ 中的归一化基态解
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06528
Qian Gao, Qun Wang, Xiaojun Chang
{"title":"Normalized ground state solutions of Schrödinger-KdV system in $mathbb{R}^3$","authors":"Qian Gao, Qun Wang, Xiaojun Chang","doi":"arxiv-2409.06528","DOIUrl":"https://doi.org/arxiv-2409.06528","url":null,"abstract":"In this paper, we study the coupled Schr\"odinger-KdV system begin{align*} begin{cases} -Delta u +lambda_1 u=u^3+beta uv~~&text{in}~~mathbb{R}^{3}, -Delta v\u0000+lambda_2 v=frac{1}{2}v^2+frac{1}{2}beta u^2~~&text{in}~~mathbb{R}^{3}\u0000end{cases} end{align*} subject to the mass constraints begin{equation*}\u0000int_{mathbb{R}^{3}}|u|^2 dx=a,quad int_{mathbb{R}^{3}}|v|^2 dx=b,\u0000end{equation*} where $a, b>0$ are given constants, $beta>0$, and the frequencies\u0000$lambda_1,lambda_2$ arise as Lagrange multipliers. The system exhibits\u0000$L^2$-supercritical growth. Using a novel constraint minimization approach, we\u0000demonstrate the existence of a local minimum solution to the system.\u0000Furthermore, we establish the existence of normalized ground state solutions.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence in the incompressible limit of the corner singularities 角奇点不可压缩极限的收敛性
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06602
Hyung Jun Choi, Seonghak Kim, Youngwoo Koh
{"title":"Convergence in the incompressible limit of the corner singularities","authors":"Hyung Jun Choi, Seonghak Kim, Youngwoo Koh","doi":"arxiv-2409.06602","DOIUrl":"https://doi.org/arxiv-2409.06602","url":null,"abstract":"In this paper, we treat the corner singularity expansion and its convergence\u0000result regarding the penalized system obtained by eliminating the pressure\u0000variable in the Stokes problem of incompressible flow. The penalized problem is\u0000a kind of the Lam'{e} system, so we first discuss the corner singularity\u0000theory of the Lam'{e} system with inhomogeneous Dirichlet boundary condition\u0000on a non-convex polygon. Considering the inhomogeneous condition, we show the\u0000decomposition of its solution, composed of singular parts and a smoother\u0000remainder near a re-entrant corner, and furthermore, we provide the explicit\u0000formulae of coefficients in singular parts. In particular, these formulae can\u0000be used in the development of highly accurate numerical scheme. In addition, we\u0000formulate coefficients in singular parts regarding the Stokes equations with\u0000inhomogeneous boundary condition and non-divergence-free property of velocity\u0000field, and thus we show the convergence results of coefficients in singular\u0000parts and remainder regarding the concerned penalized problem.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of bound states to $Δu-u+|u|^{p-1}u= 0$ in $mathbb{R}^n$, $nge 3$ 在$mathbb{R}^n$, $nge 3$中$Δu-u+|u|^{p-1}u= 0$的约束状态的唯一性
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06915
Moxun Tang
{"title":"Uniqueness of bound states to $Δu-u+|u|^{p-1}u= 0$ in $mathbb{R}^n$, $nge 3$","authors":"Moxun Tang","doi":"arxiv-2409.06915","DOIUrl":"https://doi.org/arxiv-2409.06915","url":null,"abstract":"We give a positive answer to a conjecture of Berestycki and Lions in 1983 on\u0000the uniqueness of bound states to $Delta u +f(u)=0$ in $mathbb{R}^n$, $uin\u0000H^1(mathbb{R}^n)$, $unotequiv 0$, $nge 3$. For the model nonlinearity\u0000$f(u)=-u+|u|^{p-1}u$, $1<p<(n+2)/(n-2)$, arisen from finding standing waves of\u0000Klein-Gordon equation or nonlinear Schr\"odinger equation, we show that, for\u0000each integer $kge 1$, the problem has a unique solution $u=u(|x|)$, $xin\u0000mathbb{R}^n$, up to translation and reflection, that has precisely $k$ zeros\u0000for $|x|>0$.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps 具有可变跳跃的传播波逆问题的 Lipschitz 稳定性
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06260
L BaudouinLAAS-MAC, A ImbaUTFSM, A MercadoUTFSM, A OssesCMM
{"title":"Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps","authors":"L BaudouinLAAS-MAC, A ImbaUTFSM, A MercadoUTFSM, A OssesCMM","doi":"arxiv-2409.06260","DOIUrl":"https://doi.org/arxiv-2409.06260","url":null,"abstract":"This article studies an inverse problem for a transmission wave equation, a\u0000system where the main coefficient has a variable jump across an internal\u0000interface given by the boundary between two subdomains. The main result obtains\u0000Lipschitz stability in recovering a zeroth-order coefficient in the equation.\u0000The proof is based on the Bukhgeim-Klibanov method and uses a new one-parameter\u0000global Carleman inequality, specifically constructed for the case of a variable\u0000main coefficient which is discontinuous across a strictly convex interface. In\u0000particular, our hypothesis allows the main coefficient to vary smoothly within\u0000each subdomain up to the interface, thereby extending the preceding literature\u0000on the subject.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic expansion of a nonlocal phase transition energy 非局部相变能量的渐近展开
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06215
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci, Mary Vaughan
{"title":"Asymptotic expansion of a nonlocal phase transition energy","authors":"Serena Dipierro, Stefania Patrizi, Enrico Valdinoci, Mary Vaughan","doi":"arxiv-2409.06215","DOIUrl":"https://doi.org/arxiv-2409.06215","url":null,"abstract":"We study the asymptotic behavior of the fractional Allen--Cahn energy\u0000functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s in (0,frac12)$, we establish the complete\u0000asymptotic development up to the boundary in the sense of $Gamma$-convergence.\u0000In particular, we prove that the first-order term is the nonlocal minimal\u0000surface functional while all higher-order terms are zero. For $s in [frac12,1)$, we focus on the one-dimensional case and we prove\u0000that the first order term is the classical perimeter functional plus a\u0000penalization on the boundary. Towards this end, we establish existence of\u0000minimizers to a corresponding fractional energy in a half-line, which provides\u0000itself a new feature with respect to the existing literature.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regular Strichartz estimates in Lorentz-type spaces with application to the $H^s$-critical inhomogeneous biharmonic NLS equation 洛伦兹型空间中的正规斯特里查兹估计值与对 $H^s$ 临界非均质双谐波 NLS 方程的应用
arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI: arxiv-2409.06278
RoeSong Jang, JinMyong An, JinMyong Kim
{"title":"Regular Strichartz estimates in Lorentz-type spaces with application to the $H^s$-critical inhomogeneous biharmonic NLS equation","authors":"RoeSong Jang, JinMyong An, JinMyong Kim","doi":"arxiv-2409.06278","DOIUrl":"https://doi.org/arxiv-2409.06278","url":null,"abstract":"In this paper, we investigate the Cauchy problem for the $H^s$-critical\u0000inhomogeneous biharmonic nonlinear Schr\"{o}dinger (IBNLS) equation [iu_{t}pm\u0000Delta^{2} u=lambda |x|^{-b}|u|^{sigma}u,~u(0)=u_{0} in H^{s} (mathbb\u0000R^{d}),] where $lambdain mathbb C$, $dge 3$, $1le s<frac{d}{2}$,\u0000$0<b<min left{4,2+frac{d}{2}-s right}$ and $sigma=frac{8-2b}{d-2s}$.\u0000First, we study the properties of Lorentz-type spaces such as Besov-Lorentz\u0000spaces and Triebel-Lizorkin-Lorentz spaces. We then derive the regular\u0000Strichartz estimates for the corresponding linear equation in Lorentz-type\u0000spaces. Using these estimates, we establish the local well-posedness as well as\u0000the small data global well-posedness and scattering in $H^s$ for the\u0000$H^s$-critical IBNLS equation under less regularity assumption on the nonlinear\u0000term than in the recent work cite{AKR24}. This result also extends the ones of\u0000cite{SP23,SG24} by extending the validity of $d$, $b$ and $s$. Finally, we\u0000give the well-posedness result in the homogeneous Sobolev spaces $dot{H}^s$.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"109 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信