Kinetic FRG Young Researchers Workshop
March 2-5, 2009

CSIC Building (#406), Seminar Room 4122.

Acoustic Limit for the Boltzmann Equation in Optimal Scaling

Dr. Juhi Jang

Courant Institute - New York University

Abstract:  Based on a recent L2-L∞ framework, we establish the acoustic limit of the Boltz­mann equation for general collision kernels. For a solution , where , to the rescaled Boltzmann equation

in the whole space R3 or inside a periodic box T3, we prove that Gε converge to G whose dynamics is governed by the acoustic system, as δ = δ(ε), ε, ε/δ → 0. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.

The results have been done in collaboration with Yan Guo and Ning Jiang.