Abstract
We prove rather general L ∞ bounds for hydrodynamical fields in terms of weighted L ∞ norms of the kinetic density. We use these estimates to prove L ∞ bounds and uniqueness for the solution of the BGK Equation, which is a simple relaxation model introduced by Bhatnagar, Gross & Krook to mimic Boltzmann flows.
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References
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Communicated by L. Arkeryd
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Perthame, B., Pulvirenti, M. Weighted L∞ bounds and uniqueness for the Boltzmann BGK model. Arch. Rational Mech. Anal. 125, 289–295 (1993). https://doi.org/10.1007/BF00383223
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DOI: https://doi.org/10.1007/BF00383223