Formation of singularity for the rotating shallow water system

TL;DR

This paper studies how singularities form in the rotating shallow water system, analyzing conditions for their development or prevention in radially symmetric solutions through moment analysis and initial data considerations.

Contribution

It provides new proofs of singularity formation and global existence criteria for radially symmetric solutions of the rotating shallow water system.

Findings

Singularity formation is proved via moment analysis.

Singularity occurs for initial data with compact support.

Conditions for global existence are characterized for separated variable solutions.

Abstract

In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study for the associated moments for two dimensional solutions. For the radial symmetric solutions, the formation of singularity is established for the initial data with compact support. Finally, the global existence or formation of singularity for the radial symmetric solutions of the rotating shallow water system are analyzed in detail when the solutions are of the form with separated variables.