Persistence of global well-posedness for the 2D Boussinesq equations with fractional dissipation

Abstract

In this paper, we study the IBVP for the 2D Boussinesq equations with fractional dissipation in the subcritical case, and prove the persistence of global well-posedness of strong solutions. Moreover, we also prove the long time decay of the solutions, and investigate the existence of the solutions in Sobolev spaces W 2,p (R 2) × W 1,p (R 2) for some p > 2.

Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain

“…Very recently, Ye [40] studied the nonhomogeneous density-temperature-dependent Boussinesq equations with zero diffusivity over bounded domains and obtained a blow-up criterion in terms of the gradient of viscosity for strong solutions with vacuum. Global well-posedness with fractional partial dissipation can be found in recent works [2,14,30,39,41,44]. For local and global theories of solutions in a three-dimensional space, we refer to [3,4,12,16,23,26,29,36,38] and the references cited therein.…”