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.

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We study the existence and uniqueness of weak solutions and the existence of global attractors to a class of semilinear parabolic equations involving the Grushin operator and nonlinearities of arbitrary order. The main novelty of our result is that no restriction on the upper growth of the nonlinearities is imposed