Incompressible Boussinesq equations and borderline Besov spaces

TL;DR

This paper establishes local-in-time existence and uniqueness results for an inviscid Boussinesq system with diffusive density, using initial data in borderline Besov spaces, advancing the mathematical understanding of such fluid models.

Contribution

It proves the well-posedness of the Boussinesq system under new conditions involving borderline Besov spaces and diffusive density, which was not previously established.

Findings

Existence and uniqueness of solutions for the system.

Results hold for initial data in borderline Besov spaces.

Addresses the role of density diffusion in the system.

Abstract

We prove local-in-time existence and uniqueness of an inviscid Boussinesq-type system. We assume the density equation contains nonzero diffusion and that our initial vorticity and density belong to a space of borderline Besov type.