Boundary layer problem: Navier-Stokes equations and Euler equations
by Fernanda Cipriano (GFMUL / Departamento de Matemática, FCTUNL, Portugal)
We consider the flow of an incompressible viscous fluid in a 2D-bounded domain, with flux through the boundary. The flow is described by the Navier-Stokes equations with a non-homogeneous boundary condition also known as Yudovich condition.
We prove that the vanishing viscosity limit of the solutions of the Navier-Stokes equations is a solution of the Euler equations satisfying the Yudovich condition on the inflow region of the boundary.
This is a joint work with Nikolai Chemetov.