2008/05/07 by Eric A. Carlen, José A. Carrillo, Jose A. Carrillo +1 · 17 citations
Mathematics · Physics and Astronomy · #Convergence (economics) #Dissipative system #Distribution (mathematics) #Gas Dynamics and Kinetic Theory #Homogeneous #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Norm (philosophy) #Sobolev space #State (computer science) #math-ph #math.MP #msc:35B40 #msc:82C40
paper · pdf · doi:10.1016/j.anihpc.2008.10.005
published in Annales de l Institut Henri Poincaré C Analyse Non Linéaire 26(5), 1675-1700 (Elsevier BV) · 2 figures
arxiv created 2008/05/07 · openalex publication_date 2008/12/05 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogeneous cooling state present in the literature implies the strong convergence in Sobolev norms and in the L1 norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the L1 distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.