Blowup of Solutions of the Hydrostatic Euler Equations

TL;DR

This paper proves that smooth solutions to the hydrostatic Euler equations can develop singularities in finite time for specific initial conditions, highlighting limitations of solution regularity.

Contribution

It establishes finite-time blowup results for a class of initial data in the hydrostatic Euler equations, advancing understanding of solution behavior.

Findings

Finite-time blowup for certain initial data

Conditions leading to solution singularity

Implications for fluid dynamics models

Abstract

In this paper we prove that for a certain class of initial data, smooth solutions of the hydrostatic Euler equations blow up in finite time.