Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Boundary correctors and energy estimates for the boundary layer problem

Helena Lopes

Universidade Federal do Rio de Janeiro

In a short note in 1984 T. Kato established a criterion for the vanishing viscosity limit to hold in the presence of boundaries, namely that the energy dissipation must vanish in a small region near the boundary, as viscosity tends to zero. The proof is based on the use of a boundary corrector and energy estimates. In this talk, we will discuss Kato's result and its relation to the physical phenomenon of the boundary layer. We then describe the application of these boundary correctors to several different scenarios involving boundary layers, including small obstacles, large domains, Euler-alpha and second grade fluids.