Lemmes de moments, de moyenne et de dispersion. (Moments, averaging and dispersion lemmas). (French. Abridged English version) Zbl 0761.35085

Lions, Pierre-Louis; Perthame, Benoît

C. R. Acad. Sci., Paris, Sér. I 314, No. 11, 801-806 (1992).

Summary: We prove some new moments lemmas for transport equations from which we deduce a new proof of the averaging lemmas. Thanks to the Wigner transform, we also deduce dispersion lemmas for the Schrödinger equation which unify and sometimes improve the known results on the regularizing effects of order 1/2.

MSC:

35Q35	PDEs in connection with fluid mechanics
82C31	Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q40	PDEs in connection with quantum mechanics

Keywords:

Vlasov-Poisson equation; transport equations; Schrödinger equation