Local Well-Posedness of Solutions to the 2D Mixed Prandtl Equations in a Sobolev Space Without Monotonicity and Lower Bound
摘要
In this chapter, we shall investigate the 2D Prandtl-Shercliff regime equations on the half plane and prove the local existence and uniqueness of solutions for any initial datum by using the classical energy methods in a Sobolev space. Compared to the existence and uniqueness of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays a key role, this monotonicity condition is not needed for the 2D mixed Prandtl equations.