The Boundary Layer Expansions of the Steady 2D Boussinesq Equations With a Moving Boundary

ABSTRACT This article demonstrates the validity of the boundary layer expansions of the steady Boussinesq system in the domain . At the boundary , we consider the slip boundary condition for the tangential velocity field, along with the nonhomogeneous Dirichlet boundary condition for the temperature field. We justify the expansions at any order, which generalizes the results of Guo et al. (Annals of PDE, 2017) and Li et al. (Journal of Differential Equations, 2020), obtained for the Navier–Stokes equations, to the Boussinesq system.