Long time dynamics of layered solutions to the shallow water equations

被引：0
作者：
Marta Strani
机构：
[1] Institut de Mathématiques de Jussieu,Université Paris
来源：
Bulletin of the Brazilian Mathematical Society, New Series | 2016年 / 47卷
关键词：
shallow water; viscous fluids; Navier-Stokes equations; existence; uniqueness; regularity theory; initial-boundary; 35Q35; 76D03; 76D05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the existence of a positive connection, i.e. a stationary solution connecting the boundary data, for the initial-boundary value problem for the viscous shallow water system in a bounded interval (−ℓ, ℓ) of the real line. Subsequently, we investigate the asymptotic behavior of the time-dependent solutions, showing that they first develop into a layered function and then they drift towards the steady state in an exponentially long time interval. The main tool of our analysis is given by the derivation of an ODE for the interface location.
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页码：765 / 777
页数：12
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