From the Kinetic Theory of Gases to Continuum Mechanics

François Golse (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions

Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like that of an incompressible fluid with constant density.

Mots clés: Hydrodynamic limits; Kinetic models; Boltzmann equation; Entropy production; Euler equations; Navier-Stokes equations

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

François Golse. From the Kinetic Theory of Gases to Continuum Mechanics. Harold Grad Lecture; 27th International Symposium on Rarefied Gas Dynamics, Jul 2010, Pacific Grove, CA, United States. pp.15-27, ⟨10.1063/1.3562621⟩. ⟨hal-00512869⟩