Well-posedness and inviscid limits of the Boussinesq equations with fractional Laplacian dissipation

Abstract

This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regularity of a general system of d-dimensional Boussinesq equations to that of its formal inviscid limit. The third obtains the global existence, uniqueness and inviscid limit of a system of 2D Boussinesq equations with the Yudovich-type initial data.