Speaker: Researcher Chengjie Liu(Shanghai jiao Tong University )

Title:Prandtl boundary layer theory for MHD equations in Sobolev spaces without monotonicity

Time: Fri, June.1, 2018 , PM:4:40-5:40.

Location: Room 4224, Building No.4, Wushan Campus

Abstract:

  In the joint work with Feng Xie and Tong Yang, we study the validity of the Prandtl boundary layer theory for MHD equations in the half plane with no-slip boundary conditions on the velocity vector and the perfect conducting boundary conditions on the magnetic field. In the case that viscosity and magnetic diffusion tend to zero simultaneously, we derive the boundary layer problem and establish the well-posedness result in Sobolev spaces under the assumption of nonzero tangential magnetic field, without any monotonicity assumption on the velocity. Then, when the initial tangential magnetic field of MHD doesn't vanish at the boundary, we justify the validity of corresponding Prandtl boundary layer expansions in the Sobolev framework. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics.