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
收藏
页码：96 / 148
页数：53
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