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Weighted \(L^ \infty\) bounds and uniqueness for the Boltzmann BGK model. (English) Zbl 0786.76072

Summary: We prove rather general \(L^ \infty\) bounds for hydrodynamical fields in terms of weighted \(L^ \infty\) norms of the kinetic density. We use these estimates to prove \(L^ \infty\) bounds and uniqueness for the solution of the BGK equation, which is a simple relaxation model to mimic Boltzmann flows.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76A02 Foundations of fluid mechanics
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[1] P. L. Bhatnagar, E. P. Gross & M. Krook, A model for collision processes in gases, Phys. Rev. 94, 511-514 (1954). · Zbl 0055.23609 · doi:10.1103/PhysRev.94.511
[2] B. Perthame, Global existence to the BGK model of Boltzmann Equation, J. Diff. Eq. 82, 191-205 (1989). · Zbl 0694.35134 · doi:10.1016/0022-0396(89)90173-3
[3] W. Greenberg & J. Polewczak, A gobal existence theorem for the nonlinear BGK equation, J. Stat. Phys. 55, 1313-1321 (1989). · Zbl 0714.60110 · doi:10.1007/BF01041091
[4] R. DiPerna & P. L. Lions, On the Cauchy problem for the Boltzmann equation, Ann. of Math. 130, 321-366 (1989). · Zbl 0698.45010 · doi:10.2307/1971423
[5] E. Ringeissen, Thesis, University of Paris VII, 1991.
[6] B. Khobalatte & B. Perthame, Maximum principle on the entropy and second order kinetic schemes for gas dynamics equations. To appear in Math. Comp. (1994). · Zbl 0795.35085
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