Velocity averaging in \(L^1\) for the transport equation. (English. Abridged French version) Zbl 1154.35326

Summary: A new result of \(L^1\)-compactness for velocity averages of solutions to the transport equation is stated and proved in this Note. This result, proved by a new interpolation argument, extends to the case of any space dimension Lemma 8 of F. Golse, P. L. Lions, B. Perthame and R. Sentis, J. Funct. Anal. 76, 110–125 (1988; Zbl 0652.47031)], proved there in space dimension 1 only. This is a key argument in the proof of the hydrodynamic limits of the Boltzmann or BGK equations to the incompressible Euler or Navier-Stokes equations.


35F20 Nonlinear first-order PDEs
35Q35 PDEs in connection with fluid mechanics
82C70 Transport processes in time-dependent statistical mechanics


Zbl 0652.47031
Full Text: DOI


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