On the Existence and Uniqueness of Solutions to 2d G-Bénard Problem in Unbounded Domains

Abstract

We consider the 2D g-Bénard problem in domains satisfying the Poincaré inequality with homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of global weak solutions. The obtained results particularly extend previous results for 2D g-Navier-Stokes equations and 2D Bénard problem.