Local well-posedness for Boussinesq approximation with shear dependent viscosities in 3D

Abstract

In this paper, we prove the existence and uniqueness of regular weak solutions for a nonlinear Boussinesq system in a small time interval. The viscosity is assumed to be with a p-structure depending on the shear rate. We mainly work on 3D case with periodic boundary and initial value conditions. The W2,p-type regularity for velocity and H2-type regularity for temperature were obtained for 75<p≤2.