Navier-Stokes Limit of Boltzmann Equation in Bounded Domain

Ning Jiang
Courant institute
New York University

Abstract: We establish a Navier-Stokes-Fourier limit for solutions to the Boltzmann equation in bounded domain. Employing the techniques in the work of Dejardins-Grenier-Linos-Masmoudi on the incompressible limit of isentropic Navier-Stokes equations with Dirichlet boundary condition, we show that the geometry of the domain plays an essential role in the convergence proof. The boundary layers and the fast acoustic waves cancelate thus the strong convergence can be established.