Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
September 21-25, 2009

CSIC Building (#406), Seminar Room 4122.

On acoustic limits from the Boltzmann equation

Dr. Ning Jiang

Courant Institute

Abstract:  In this talk, I will review the recent progress on the acoustic limits from Boltzmann equation in the bounded domain. We have two approached. The first is from DiPerna-Lions renormalized solution of the Boltzmann equation, we can justify that in the bounded domain, with some restriction on the size of fluctuation. This work is joint with Levermore and Masmoudi. The second is for linear Boltzmann equation in the bounded domain, we develop a theory kinetic-fluid coupled boundary layers, both in the acoustic and incompresisble regimes, we develop a higher order acoustic dynamics, which is governed by compressible Stokes system with different boundary conditions which depend on the accommandation coefficients. This is a joint work with Masmoudi.