Local Hilbert expansion for the Boltzmann equation. (English) Zbl 1372.76089
Summary: We revisit the classical work of R. E. Caflisch [Commun. Pure. Appl. Math. 33, 651–666 (1980; Zbl 0424.76060)] for compressible Euler limit of the Boltzmann equation. By using a new \(L^2\)-\(L^\infty\) method, we prove the validity of the Hilbert expansion before shock formations in the Euler system with moderate temperature variation.
MSC:
76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
35L67 | Shocks and singularities for hyperbolic equations |
82C40 | Kinetic theory of gases in time-dependent statistical mechanics |