Long-time solvability for the 2D inviscid Boussinesq equations with borderline regularity and dispersive effects

2022/09/14 by Angulo-Castillo, Vladimir, Ferreira, Lucas C. F., Kosloff, Leonardo · 1 citation
#35A01 #35Q35 #46E35 #76B03 #76U05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.06969

Abstract

We are concerned with the long-time solvability for 2D inviscid Boussinesq equations for a larger class of initial data which covers the case of borderline regularity. First we show the local solvability in Besov spaces uniformly with respect to a parameter κ associated with the stratification of the fluid. Afterwards, employing a blow-up criterion and Strichartz-type estimates, the long-time solvability is obtained for large κ regardless of the size of initial data.

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• The effect of linear stratification on the stability of a rest state in the 2D inviscid Boussinesq system

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