Strong convergence towards homogeneous cooling states for dissipative Maxwell models |
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| Authors: | Eric A Carlen Jos A Carrillo Maria C Carvalho |
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| Institution: | aDepartment of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA;bInstitució Catalana de Recerca i Estudis Avançats and Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain;cCMAF and Departamento de Matematica da Faculdade de Ciências da Universidade de Lisboa, 1640-003 Lisboa, Portugal |
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| Abstract: | 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. |
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| Keywords: | Dissipative Maxwell models Propagation of regularity Long time asymptotics Self-similarity Strong convergence Small inelasticity limit |
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