The nonlinear 2D subcritical inviscid shallow water equations with periodicity in one direction

Aimin Huang; Roger Temam

doi:10.3934/cpaa.2014.13.2005

Article Contents

2014, Volume 13, Issue 5: 2005-2038. Doi: 10.3934/cpaa.2014.13.2005

This issue Previous Article Totally dissipative dynamical processes and their uniform global attractors Next Article An extension of the Fitzpatrick theory

The nonlinear 2D subcritical inviscid shallow water equations with periodicity in one direction

Aimin Huang^1, and
Roger Temam^2,

1.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405
2.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, 47205

Received: August 2013

Revised: January 2014

Published: September 2015

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Abstract

In continuation with earlier works on the shallow water equations in a rectangle [10, 11], we investigate in this article the fully inviscid nonlinear shallow water equations in space dimension two in a rectangle $(0,1)_x \times (0,1)_y$. We address in this article the subcritical case, corresponding to the condition (3) below. Assuming space periodicity in the $y$-direction, we propose the boundary conditions for the $x$-direction which are suited for the subcritical case and develop, for this problem, results of existence, uniqueness and regularity of solutions locally in time for the corresponding initial and boundary value problem.

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Mathematics Subject Classification: Primary: 76B03, 76B15; Secondary: 58J45.

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