We improve in three ways the results of  that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation. First, we enlarge the class of collision kernels treated to that found in , thereby treating all classical collision kernels to which the DiPerna-Lions theory applies. Second, we improve the scaling of the kinetic density fluctuations with Knudsen number from O(εm) for some m > 1/2 to (ε1/2. Third, we extend the results from periodic domains to bounded domains with a Maxwell reflection boundary condition, deriving the impermeable boundary condition for the acoustic system.
- Acoustic limit
- Boltzmann equation
- Renormalized boundary condition
ASJC Scopus subject areas
- Applied Mathematics