发布求助
文献互助 智能选刊 最新文献

arXiv: Analysis of PDEs最新文献

筛选
英文 中文
Principal Frequency of $p$-Sub-Laplacians for General Vector Fields 一般向量场的$p$-子拉普拉斯算子的主频率
arXiv: Analysis of PDEs Pub Date : 2020-08-13 DOI: 10.4171/ZAA/1674
Michael Ruzhansky, Bolys Sabitbek, D. Suragan
{"title":"Principal Frequency of $p$-Sub-Laplacians for General Vector Fields","authors":"Michael Ruzhansky, Bolys Sabitbek, D. Suragan","doi":"10.4171/ZAA/1674","DOIUrl":"https://doi.org/10.4171/ZAA/1674","url":null,"abstract":"In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet p-sub-Laplacian for general vector fields. As a byproduct, we establish the Caccioppoli inequalities and also discuss the particular cases on the Grushin plane and on the Heisenberg group.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73911508","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: 2
Anisotropic regularity of linearized compressible vortex sheets 线性化可压缩涡旋片的各向异性规律
arXiv: Analysis of PDEs Pub Date : 2020-08-12 DOI: 10.1142/s0219891620500113
P. Secchi
{"title":"Anisotropic regularity of linearized compressible vortex sheets","authors":"P. Secchi","doi":"10.1142/s0219891620500113","DOIUrl":"https://doi.org/10.1142/s0219891620500113","url":null,"abstract":"We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation which describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if $|[vcdottau]|>2sqrt{2},c$, and the well-posedness was obtained in standard weighted Sobolev spaces. \u0000The aim of the present paper is to improve the result of [10], by showing the existence of the solution in function spaces with some additional weighted anisotropic regularity in the frequency space.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74287746","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
On the interaction of metric trapping and a boundary 度量俘获与边界的相互作用
arXiv: Analysis of PDEs Pub Date : 2020-08-12 DOI: 10.1090/PROC/15460
K. Datchev, Jason Metcalfe, Jacob Shapiro, M. Tohaneanu
{"title":"On the interaction of metric trapping and a boundary","authors":"K. Datchev, Jason Metcalfe, Jacob Shapiro, M. Tohaneanu","doi":"10.1090/PROC/15460","DOIUrl":"https://doi.org/10.1090/PROC/15460","url":null,"abstract":"By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as the boundary passes through the trapped set, one goes from a nontrapping scenario where lossless local energy estimates are available for the wave equation to the case of stably trapped rays where all but a logarithmic amount of decay is lost.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89577297","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
The spatially homogeneous Boltzmann equation for massless particles in an FLRW background FLRW背景下无质量粒子的空间齐次玻尔兹曼方程
arXiv: Analysis of PDEs Pub Date : 2020-08-09 DOI: 10.1063/5.0037951
Ho Lee
{"title":"The spatially homogeneous Boltzmann equation for massless particles in an FLRW background","authors":"Ho Lee","doi":"10.1063/5.0037951","DOIUrl":"https://doi.org/10.1063/5.0037951","url":null,"abstract":"We study the spatially homogeneous relativistic Boltzmann equation for massless particles in an FLRW background with scattering kernels in a certain range of soft and hard potentials. We obtain the future global existence of small solutions in a weighted $L^1cap L^infty$ space.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90202120","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: 1
Higher-order asymptotic profiles of the solutions to the viscous Fornberg–Whitham equation 粘性Fornberg-Whitham方程解的高阶渐近分布
arXiv: Analysis of PDEs Pub Date : 2020-08-06 DOI: 10.1016/j.na.2020.112200
I. Fukuda, Kenta Itasaka
{"title":"Higher-order asymptotic profiles of the solutions to the viscous Fornberg–Whitham equation","authors":"I. Fukuda, Kenta Itasaka","doi":"10.1016/j.na.2020.112200","DOIUrl":"https://doi.org/10.1016/j.na.2020.112200","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88221763","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: 2
Large-amplitude internal fronts in two-fluid systems 双流体系统中的大振幅内锋面
arXiv: Analysis of PDEs Pub Date : 2020-07-31 DOI: 10.5802/crmath.128
R. Chen, Samuel Walsh, Miles H. Wheeler
{"title":"Large-amplitude internal fronts in two-fluid systems","authors":"R. Chen, Samuel Walsh, Miles H. Wheeler","doi":"10.5802/crmath.128","DOIUrl":"https://doi.org/10.5802/crmath.128","url":null,"abstract":"In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incompressible Euler equation in two dimensions. The fluids are bounded above and below by flat horizontal walls and acted upon by gravity. We obtain continuous curves of solutions to this system that bifurcate from the trivial solution where the interface is flat. Following these families to the their extreme, the internal interface either overturns, comes into contact with the upper wall, or develops a highly degenerate \"double stagnation\" point. \u0000Our construction is made possible by a new abstract machinery for global continuation of monotone front-type solutions to elliptic equations posed on infinite cylinders. This theory is quite robust and, in particular, can treat fully nonlinear equations as well as quasilinear problems with transmission boundary conditions.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74306916","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: 3
Decay of Strong Solution for the Compressible Navier-Stokes Equations with Large Initial Data 具有大初始数据的可压缩Navier-Stokes方程强解的衰减
arXiv: Analysis of PDEs Pub Date : 2020-07-27 DOI: 10.1016/J.NA.2021.112494
Jincheng Gao, Zhengzhen Wei, Z. Yao
{"title":"Decay of Strong Solution for the Compressible Navier-Stokes Equations with Large Initial Data","authors":"Jincheng Gao, Zhengzhen Wei, Z. Yao","doi":"10.1016/J.NA.2021.112494","DOIUrl":"https://doi.org/10.1016/J.NA.2021.112494","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77701409","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: 3
Existence and symmetry of solutions to 2-D Schrödinger–Newton equations 二维Schrödinger-Newton方程解的存在性与对称性
arXiv: Analysis of PDEs Pub Date : 2020-07-25 DOI: 10.4310/DPDE.2021.v18.n2.a3
D. Cao, Wei Dai, Yang Zhang
{"title":"Existence and symmetry of solutions to 2-D Schrödinger–Newton equations","authors":"D. Cao, Wei Dai, Yang Zhang","doi":"10.4310/DPDE.2021.v18.n2.a3","DOIUrl":"https://doi.org/10.4310/DPDE.2021.v18.n2.a3","url":null,"abstract":"In this paper, we consider the following 2-D Schr\"{o}dinger-Newton equations begin{eqnarray*} -Delta u+a(x)u+frac{gamma}{2pi}left(log(|cdot|)*|u|^pright){|u|}^{p-2}u=b{|u|}^{q-2}u qquad text{in} ,,, mathbb{R}^{2}, end{eqnarray*} where $ain C(mathbb{R}^{2})$ is a $mathbb{Z}^{2}$-periodic function with $inf_{mathbb{R}^{2}}a>0$, $gamma>0$, $bgeq0$, $pgeq2$ and $qgeq 2$. By using ideas from cite{CW,DW,Stubbe}, under mild assumptions, we obtain existence of ground state solutions and mountain pass solutions to the above equations for $pgeq2$ and $qgeq2p-2$ via variational methods. The auxiliary functional $J_{1}$ plays a key role in the cases $pgeq3$. We also prove the radial symmetry of positive solutions (up to translations) for $pgeq2$ and $qgeq 2$. The corresponding results for planar Schr\"{o}dinger-Poisson systems will also be obtained. Our theorems extend the results in cite{CW,DW} from $p=2$ and $b=1$ to general $pgeq2$ and $bgeq0$.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89760044","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: 11
On endpoint regularity criterion of the 3D Navier–Stokes equations 三维Navier-Stokes方程的端点正则性准则
arXiv: Analysis of PDEs Pub Date : 2020-07-24 DOI: 10.4310/DPDE.2021.V18.N1.A5
Zhouyu Li, D. Zhou
{"title":"On endpoint regularity criterion of the 3D Navier–Stokes equations","authors":"Zhouyu Li, D. Zhou","doi":"10.4310/DPDE.2021.V18.N1.A5","DOIUrl":"https://doi.org/10.4310/DPDE.2021.V18.N1.A5","url":null,"abstract":"Let $(u, pi)$ with $u=(u_1,u_2,u_3)$ be a suitable weak solution of the three dimensional Navier-Stokes equations in $mathbb{R}^3times [0, T]$. Denote by $dot{mathcal{B}}^{-1}_{infty,infty}$ the closure of $C_0^infty$ in $dot{B}^{-1}_{infty,infty}$. We prove that if $uin L^infty(0, T; dot{B}^{-1}_{infty,infty})$, $u(x, T)in dot{mathcal{B}}^{-1}_{infty,infty})$, and $u_3in L^infty(0, T; L^{3, infty})$ or $u_3in L^infty(0, T; dot{B}^{-1+3/p}_{p, q})$ with $3<p, q< infty$, then $u$ is smooth in $mathbb{R}^3times [0, T]$. Our result improves a previous result established by Wang and Zhang [Sci. China Math. 60, 637-650 (2017)].","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77319122","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: 1
Interior $C^2$ estimate for Monge-Ampère equation in dimension two 二维monge - ampantere方程的内部C^2估计
arXiv: Analysis of PDEs Pub Date : 2020-07-22 DOI: 10.1090/PROC/15459
Jiakun Liu
{"title":"Interior $C^2$ estimate for Monge-Ampère equation in dimension two","authors":"Jiakun Liu","doi":"10.1090/PROC/15459","DOIUrl":"https://doi.org/10.1090/PROC/15459","url":null,"abstract":"We obtain a genuine local $C^2$ estimate for the Monge-Ampere equation in dimension two, by using the partial Legendre transform.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87938785","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: 3
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