Global well-posedness for the 2D Boussinesq equations with a velocity damping term

Abstract

In this paper, we prove global well-posedness of smooth solutions to the two-dimensional incompressible Boussinesq equations with only a velocity damping term when the initial data is close to an nontrivial equilibrium state $(0,x_2)$. As a by-product, under this equilibrium state, our result gives a positive answer to the question proposed by [ACWX] (see P.3597).

The final version, DCDS-A (to appear)

References in corpus (1)

• Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems