Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
Florent Berthelin, François Bouchut (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Displaying similar documents to “On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws”
Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
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Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.
Cédric Villani (1999)
Revista Matemática Iberoamericana
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We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L(R) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.