On the radius of spatial analyticity for the inviscid Boussinesq equations

TL;DR

This paper investigates the persistence and quantification of spatial analyticity in solutions to the inviscid Boussinesq equations, establishing lower bounds on the analyticity radius over time.

Contribution

It provides a novel inductive method to derive lower bounds on the spatial analyticity radius for solutions with real-analytic initial data.

Findings

Solutions remain real-analytic during their existence interval.

Lower bounds on the radius of analyticity are explicitly obtained.

The method applies to smooth solutions of the inviscid Boussinesq equations.

Abstract

In this paper, we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations. If the initial datum is real-analytic, the solution remains real-analytic on the existence interval. By an inductive method we can obtain lower bounds on the radius of spatial analyticity of the smooth solution.