Boundary Value Problems and Multiscale Coupling Methods for Kinetic Equations

Invariant Manifolds for Stationary Boltzmann Equation and Applications

Tai-Ping Liu

Stanford University

With Shih-Hsien Yu, we study the invariant manifolds for stationary Boltzmann equation and apply the theory to the construction of the boundary layers. Of particular interest is coupling of the boundary Knusden-type boundary layer and the interior fluid-like waves when the Mach number is around one or zero. Our Green's function approach allows for strong quantitative estimates required for the strongly nonlinear phenomena of resonance.