Local well-posedness to the thermal boundary layer equations in Sobolev space

Abstract

In this paper, we study the local well-posedness of the thermal boundary layer equations for the two-dimensional incompressible heat conducting flow with nonslip boundary condition for the velocity and Neumann boundary condition for the temperature. Under Oleinik's monotonicity assumption, we establish the local-in-time existence and uniqueness of solutions in Sobolev space for the boundary layer equations by a new weighted energy method developed by Masmoudi and Wong.

Keywords

• thermal boundary layer equations
• oleinik's monotonicity condition
• local well-posedness