Viscosity analysis on the spatially homogeneous Boltzmann equation

Article type: Research Article

Authors: Zheng, Minling^; | Yang, Xiaoping

Affiliations: School of Science, Nanjing University of Science & Technology, Nanjing 210094, Jiangsu, P.R. China E-mail: [email protected] | School of Science, Huzhou Teacher College, Huzhou 313000, Zhejiang, P.R. China E-mail: [email protected]

Abstract: 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*|γb(cos θ) and δ>0 small enough; especially show that the solution f can approach the one of unperturbed equation in Lk1-norm while δ goes to 0. Our method mainly relies on the interpolation inequalities and the decomposition of Q+.

Keywords: weak solution, viscosity Boltzmann equation, dispersion coefficients, collision kernel

Journal: Asymptotic Analysis, vol. 53, no. 1-2, pp. 13-28, 2007