We consider a kinetic model whose evolution is described by a Boltzmann- like equation for the one-particle phase space distribution f(x,v,t). There are hard-sphere collisions between the particles as well as collisions with randomly xed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled fε(x,v,t) = f(ε−1x,v,ε−2t) tends, as ε → 0, to a Maxwellian Mρ,0,T = ρ 3/2 exp[− |v|2 ], where ρ and T are solutions of coupled diffusion (2πT) 2T equations and estimate the error in Lx2,v.
Esposito, R., Garrido, P.l., Lebowitz, J.l., Marra, R. (2019). Diffusive limit for a Boltzmann-like equation with non-conserved momentum. NONLINEARITY, 32(12), 4834-4852 [10.1088/1361-6544/ab395a].
Diffusive limit for a Boltzmann-like equation with non-conserved momentum
Marra, R
2019-01-01
Abstract
We consider a kinetic model whose evolution is described by a Boltzmann- like equation for the one-particle phase space distribution f(x,v,t). There are hard-sphere collisions between the particles as well as collisions with randomly xed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled fε(x,v,t) = f(ε−1x,v,ε−2t) tends, as ε → 0, to a Maxwellian Mρ,0,T = ρ 3/2 exp[− |v|2 ], where ρ and T are solutions of coupled diffusion (2πT) 2T equations and estimate the error in Lx2,v.File | Dimensione | Formato | |
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