Viscosity analysis on the spatially homogeneous Boltzmann equation

In this paper we study the existence and uniqueness of the solution to the viscosity equation ∂tf = δΔf + Q(f , f ) with collision kernel B(|v − v∗|, ω) = |v − v∗| γ b(cos θ )a nd δ> 0 small enough; especially show that the solution f can approach the one of unperturbed equation in L 1 -norm while δ goes to 0. Our method mainly relies on the interpolation inequalities and the decomposition of Q + .

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