Uniform L^p-stability estimate for the spatially inhomogeneous Boltzmann equation near vacuum

We present a new uniform L^p-stability theory for the spatially inhomogeneous Boltzmann equation near vacuum via the nonlinear functional approach proposed by the first author. Our stability analysis is based on new nonlinear functionals which are equivalent to the p th power of L^p-distance. The L¹-nonlinear functionals play the key role of "modulators" which make the accumulative functional be non-increasing in time t along classical solutions.