Global regularity and stability of solutions to the 3D double-diffusive convection system with Navier boundary conditions

Abstract

This paper is concerned with the initial-boundary value problem to 3D double-diffusive convection system. First, we establish the global weak solutions for the double-diffusive convection system in a domain $\Omega$ with Navier boundary condition by Galerkin approximation method. Then by making higher-order estimates of the approximation function with higher regularity assumption on the initial data, combined with compactness argument we obtain the local strong solution with uniqueness. Secondly, we obtain the classical Serrin-type blow-up criterion for the local strong solution in the Lorentz space. Lastly, we focus on global stability of strong large solutions for the double- diffusive convection system with Navier boundary conditions, it is shown that the large solution is stable with the additional assumption on some suitable integrable property of solution.