Convergence of solutions to the Boltzmann equation in the incompressible Euler limit. (English) Zbl 1016.76071

Saint-Raymond, Laure

Arch. Ration. Mech. Anal. 166, No. 1, 47-80 (2003).

Summary: We consider the problem of deriving rigorously, for well-prepared initial data and without any additional assumption, dissipative or smooth solutions of incompressible Euler equations from renormalized solutions of Boltzmann equation. This completes the partial results obtained by F. Bouchut, F. Golse and M. Pulvirenti [Kinetic equations and asymptotic theory. Ed. by B. Perthame and L. Desvillettes. Series in Applied Mathematics (Paris). 4. Paris: Gauthier-Villars/Elsevier. 162 p. (2000; Zbl 0979.82048)] and P.-L. Lions and N. Masmoudi [Arch. Ration. Mech. Anal. 158, 173-193, 195-211 (2001; Zbl 0987.76088)].

MSC:

76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
45K05	Integro-partial differential equations
82B40	Kinetic theory of gases in equilibrium statistical mechanics
76A02	Foundations of fluid mechanics

Keywords:

convergence; incompressible Euler limit; Boltzmann equation

Citations:

Zbl 0979.82048; Zbl 0987.76088