Well-posedness of the water-wave with viscosity problem

被引：3

作者：

Granero-Belinchon, Rafael ^{[1
]}

Scrobogna, Stefano ^{[2
]}

机构：

[1] Univ Cantabria, Dept Matemat Estadist & Comp, Santander, Spain

[2] Univ Seville, Dept Anal Matemat, Seville, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 276卷

基金：

欧洲研究理事会;

关键词：

Damped water waves; Viscosity; Well-posedness; Cross-diffusion system; FREE-SURFACE FLOWS; FLUID LAYER; MODEL;

D O I：

10.1016/j.jde.2020.12.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other hand, we establish the global well-posedness in Wiener spaces for a sufficiently large viscosity. These results are the first rigorous proofs of well-posedness for the Dias, Dyachenko & Zakharov system (Physics Letters A 2008) modeling gravity waves with viscosity when surface tension is not taken into account. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：96 / 148

页数：53

共 50 条

[1] Well-posedness and analyticity of solutions to a water wave problem with viscosity
Ngom, Marieme
Nicholls, David P.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (10) : 5031 - 5065
[2] WELL-POSEDNESS OF A MODEL FOR WATER WAVES WITH VISCOSITY
Ambrose, David M.
Bona, Jerry L.
Nicholls, David P.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2012, 17 (04): : 1113 - 1137
[3] Well-Posedness of a Model Equation for Water Waves in Fluids with Odd Viscosity
Liu, Shunlian
Ambrose, David M.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2024, 36 (04) : 3159 - 3173
[4] Global well-posedness and decay for viscous water wave models
Granero-Belinchon, Rafael
Scrobogna, Stefano
PHYSICS OF FLUIDS, 2021, 33 (10)
[5] Well-posedness for a class of mixed problem of wave equations
Liu, Haihong
Su, Ning
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (1-2) : 19 - 27
[6] Well-posedness of the Cauchy problem of a water wave equation with low regularity initial data
Wang, Hua
Cui, Shangbin
MATHEMATICAL AND COMPUTER MODELLING, 2007, 45 (9-10) : 1118 - 1132
[7] The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation
Lai, Shaoyong
Wang, Aiyin
ABSTRACT AND APPLIED ANALYSIS, 2012,
[8] Well-posedness of the Cauchy problem for a shallow water equation on the circle
Himonas, AA
Misiolek, C
JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) : 479 - 495
[9] WELL-POSEDNESS OF A PARABOLIC INVERSE PROBLEM
喻文焕
Acta Mathematicae Applicatae Sinica, 1997, (03) : 329 - 336
[10] Well-posedness of a parabolic inverse problem
Yu W.
Acta Mathematicae Applicatae Sinica, 1997, 13 (3) : 329 - 336

← 1 2 3 4 5 →