ACOUSTIC LIMIT OF THE BOLTZMANN EQUATION: CLASSICAL SOLUTIONS

We study the acoustic limit from the Boltzmann equation in the frame work of classical solutions. For a solution F(epsilon) = mu + epsilon root mu f(epsilon) to the rescaled Boltzmann equation in the acoustic time scaling partial derivative(t)F(epsilon) + v.del(x)F(epsilon) = 1/epsilon Q(F(epsilon), F(epsilon)), inside a periodic box T(3), we establish the global-in-time uniform energy estimates off f(epsilon) in epsilon and prove that f(epsilon) converges strongly to f whose dynamics is governed by the acoustic system. The collision kernel Q includes hard-sphere interaction and inverse-power law with an angular cutoff.