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Initial-boundary value problem for the discrete Boltzmann equation. (English) Zbl 0721.35037

Sémin. Équations Dériv. Partielles 1988-1989, Exp. No. 3, 6 p. (1989).
Global smooth solutions are established for the Boltzmann equation \[ \partial F_ i/\partial t+V_ i\partial F_ i/\partial x=\sum_{jk\ell}(A^{ij}_{k\ell}F_ kF_{\ell}- A^{k\ell}_{ij}F_ iF_ j) \] with smooth initial data. The required a priori estimates are obtained from conservation laws and integration along characteristics.

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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