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Almost exponential decay near Maxwellian. (English) Zbl 1096.82010
The paper addresses the issue of the relaxation of general solutions to kinetic equations of the Boltzmann type (for gases) and Vlasov-Maxwell-Boltzmann (VMB) type (for plasmas) to the stationary solution corresponding to the Maxwellian distribution. The equations are considered in the three-dimensional space with periodic boundary conditions. The systems considered include the Boltzmann equation with a soft potential of the interaction between atoms, the VMB system, and the Landau-Maxwell system for relativistic charged particles. Using a family of energy estimates, the paper proves convergence of the nonstationary distributions to the Maxwellian solution with any polynomial (i.e., non-exponential) rate in time.

82B40 Kinetic theory of gases in equilibrium statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
82D05 Statistical mechanics of gases
82D10 Statistical mechanics of plasmas
Full Text: DOI
[1] DOI: 10.1007/BF01197579 · Zbl 0434.76065
[2] DOI: 10.1007/BF01197752 · Zbl 0434.76066
[3] DOI: 10.1080/03605300008821513 · Zbl 0951.35130
[4] DOI: 10.1002/1097-0312(200101)54:1<1::AID-CPA1>3.0.CO;2-Q · Zbl 1029.82032
[5] DOI: 10.1051/cocv:2002036 · Zbl 1092.82032
[6] DOI: 10.1007/s00222-004-0389-9 · Zbl 1162.82316
[7] DOI: 10.1007/s00220-002-0729-9 · Zbl 1042.76053
[8] DOI: 10.1007/s00205-003-0262-9 · Zbl 1044.76056
[9] DOI: 10.1007/s00222-003-0301-z · Zbl 1029.82034
[10] DOI: 10.1081/PDE-200059299 · Zbl 1112.76061
[11] DOI: 10.1007/s00220-004-1151-2 · Zbl 1113.82070
[12] DOI: 10.1007/s002200050631 · Zbl 0944.35066
[13] DOI: 10.3792/pja/1195519027 · Zbl 0312.35061
[14] DOI: 10.2977/prims/1195183569 · Zbl 0538.45011
[15] DOI: 10.1007/s00220-002-0777-1 · Zbl 1041.82018
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