Global Solutions to the Initial Value Problem for the Nonlinear Boltzmann Equation | Zendy

Takaaki Nishida | Zendy; Kazuo Imai | Zendy

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Global Solutions to the Initial Value Problem for the Nonlinear Boltzmann Equation

Author(s) -

Takaaki Nishida,

Kazuo Imai

Publication year - 1976

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195190965

Subject(s) - mathematics , boltzmann equation , nonlinear system , initial value problem , boltzmann constant , value (mathematics) , lattice boltzmann methods , mathematical analysis , statistics , physics , mechanics , thermodynamics , quantum mechanics

The nonlinear Boltzmann equation in the rarefied gas dynamics is investigated for the gas molecules with the cut-off hard potential in the sense of Grad. The solution to the initial value problem is proved to exist uniquely in the large in time and to have the decay order of (l + £)~8/4 as £-> + oo for the small initial data in the space Hitir\L*(x\ Lz(v)}. The decay order is improved to (l+*)~5/* by the additional assumptions on the initial data.

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