The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

François Golse (1, 2) , Laure Saint-Raymond (2, 3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions
3 DMA - Département de Mathématiques et Applications - ENS Paris

The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161 (2004)] for Maxwell molecules.

Mots clés: Hydrodynamic limit; Boltzmann equation; Hard cutoff potential; Incompressible Navier-Stokes equations; Renormalized solutions; Leray solutions

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

François Golse, Laure Saint-Raymond. The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials. 2008. ⟨hal-00308717v1⟩