The nonlinear 2D supercritical inviscid shallow water equations in a rectangle

TL;DR

This paper proves the short-term existence of smooth solutions for the inviscid 2D shallow water equations in a rectangle near a supercritical stationary flow, advancing understanding of their mathematical behavior.

Contribution

It establishes the short-term existence of smooth solutions for the inviscid 2D shallow water equations in a supercritical regime within a rectangular domain.

Findings

Short-term existence of smooth solutions proven

Analysis near supercritical stationary solutions

Mathematical framework for inviscid shallow water equations

Abstract

In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for the corresponding initial and boundary value problem.