The Maxwell problem and the Chapman projection

V. V. Palin; E. V. Radkevich

doi:10.4067/S0719-06462010000200017

Authors

V. V. Palin Department of Mech.-Math., Moscow State University, Moscow 119899, Vorobievy Gory, Russia.
E. V. Radkevich Department of Mech.-Math., Moscow State University, Moscow 119899, Vorobievy Gory, Russia.

DOI:

https://doi.org/10.4067/S0719-06462010000200017

Keywords:

closure, the state equation, the Chapman projection, matrix equation, dynamic separation, inertional manifold

Abstract

We study the large-time behavior of global smooth solutions to the Cauchy problem for hyperbolic regularization of conservation laws. An attracting manifold of special smooth global solutions is determined by the Chapman projection onto the phase space of consolidated variables. For small initial data we construct the Chapman projection and describe its properties in the case of the Cauchy problem for moment approximations of kinetic equations. The existence conditions for the Chapman projection are expressed in terms of the solvability of the Riccati matrix equations with parameter.