Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

Abstract EN

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role.

In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations.

By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressure p in the homogeneous Besov space B ̇ ∞ , ∞ 0 .