Remarks on the Acoustic Limit for the Boltzmann Equation

الأصل · EN

We use some new nonlinear estimates found in LM to improve the results of GL that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation in three ways. First, we enlarge the class of collision kernels treated to that found in LM, 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>12 to O(ε12). Third, we extend the results from periodic domains to bounded domains with impermeable boundaries, deriving the boundary condition for the acoustic system.