Initial value problem for one-dimensional rotating shallow water equations

TL;DR

This paper investigates initial value problems for a one-dimensional rotating shallow water system, establishing local and global existence results using symmetrization techniques for both the hyperbolic and regularized equations.

Contribution

It introduces a symmetrization approach to prove existence and uniqueness for the system and its regularization, advancing understanding of solution behavior.

Findings

Local existence and uniqueness for the hyperbolic system

Global existence for the regularized system

Use of symmetrization variables to analyze solutions

Abstract

In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we establish the local existence and the uniqueness of a solution to the hyperbolic system, as well as the global existence of a solution to the regularized system. In order to prove this, we use suitable variables that symmetrize the system.