Low regularity well-posedness for the viscous surface wave equation

被引：4

作者：

Ren, Xiaoxia ^{[1
]}

Xiang, Zhaoyin ^{[2
]}

Zhang, Zhifei ^{[3
,4
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[4] Peking Univ, LMAM, Beijing 100871, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 10期

基金：

中国国家自然科学基金;

关键词：

surface wave; low regularity; Stokes estimate; NAVIER-STOKES EQUATIONS; INITIAL-VALUE-PROBLEM; LARGE-TIME EXISTENCE; TENSION; DECAY;

D O I：

10.1007/s11425-018-9410-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the local well-posedness of the viscous surface wave equation in low regularity Sobolev spaces. The key points are to establish several new Stokes estimates depending only on the optimal boundary regularity and to construct a new iteration scheme on a known moving domain. Our method could be applied to some other fluid models with free boundaries.

引用

页码：1887 / 1924

页数：38

共 50 条

[1] Low regularity well-posedness for the viscous surface wave equation
Xiaoxia Ren
Zhaoyin Xiang
Zhifei Zhang
[J]. Science China Mathematics, 2019, 62 : 1887 - 1924
[2] Low regularity well-posedness for the viscous surface wave equation
Xiaoxia Ren
Zhaoyin Xiang
Zhifei Zhang
[J]. Science China Mathematics, 2019, 62 (10) : 1887 - 1924
[3] WELL-POSEDNESS AND DECAY OF THE VISCOUS SURFACE WAVE
Wu, Lei
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (03) : 2084 - 2135
[4] On the well-posedness and regularity of the wave equation with variable coefficients
Guo, Bao-Zhu
Zhang, Zhi-Xiong
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2007, 13 (04) : 776 - 792
[5] GLOBAL WELL-POSEDNESS FOR THE KAWAHARA EQUATION WITH LOW REGULARITY
Kato, Takamori
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (03) : 1321 - 1339
[6] LOW REGULARITY WELL-POSEDNESS FOR THE PERIODIC KAWAHARA EQUATION
Kato, Takamori
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (11-12) : 1011 - 1036
[7] Global well-posedness for the Benjamin equation in low regularity
Li, Yongsheng
Wu, Yifei
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (06) : 1610 - 1625
[8] Low regularity well-posedness for nonlinear wave equations
Dept. of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
不详
[J]. Xinan Jiaotong Daxue Xuebao, 2006, 1 (127-130):
[9] Well-posedness of the Cauchy problem of a water wave equation with low regularity initial data
Wang, Hua
Cui, Shangbin
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2007, 45 (9-10) : 1118 - 1132
[10] THE WELL-POSEDNESS AND REGULARITY OF A ROTATING BLADES EQUATION
Shen, Lin
Wang, Shu
Wang, Yongxin
[J]. ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 691 - 719

← 1 2 3 4 5 →