Abstract
In this paper we study the viscosity analysis of the spatially homogeneous Boltzmann equation for Maxwellian molecules. We first show that the global existence in time of the mild solution of the viscosity equation . We then study the asymptotic behaviour of the mild solution as the coefficients , and an estimate on is derived.
Highlights
In this paper we shall investigate the asymptotic properties of the solution of the viscosity Boltzmann equation for Maxwellian molecules t f Q f, f v f in 0, R3 (1)as the viscosity coefficients 0
In this paper we study the viscosity analysis of the spatially homogeneous Boltzmann equation for Maxwellian molecules
We first show that the global existence in time of the mild solution of the viscosity equation t f Q( f, f ) v f
Summary
In this paper we shall investigate the asymptotic properties of the solution of the viscosity Boltzmann equation for Maxwellian molecules t f Q f , f v f in 0, R3. ZHENG study the existence and uniqueness of the global solution of the viscosity equation (1) in time, and to estimate f f explicitly in C0 -norm. Let us mention some works about the spatially homogeneous Boltzmann equation with cutoff potential, see [3,4,5,6,7,8,9,10,11] for example. For the Maxwellian molecules Morgenstern first deduced the existence and uniqueness of the solution in L1 space [12]. We study the W 2, p estimate of f in Section 4 and deduce the following asymptotic expression f f 0 Aekt
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