François
Golse
Pure Mathematics
en
The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of Hilbert or Chapman-Enskog. The moment formalism shows that the limit leading to the incompressible Navier-Stokes equations, like that leading to the compressible Euler equations, is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible Navier-Stokes equations. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution of the classical Boltzmann equation and the Leray solution of the Navier-Stokes equations is discussed.
2019-04-11T13:27
1991-04-01
323-344
http://link.springer.com/10.1007/BF01026608
Fluid dynamic limits of kinetic equations. I. Formal derivations
1991-04
articles
research_article
https://scigraph.springernature.com/explorer/license/
false
Paris Diderot University
Département de Mathématiques, Université Paris VII, 755251, Paris Cédex 05, France
Mathematical Sciences
pub.1034122195
dimensions_id
1572-9613
0022-4715
Journal of Statistical Physics
63
1-2
a28c2d6954dd8cb0e8e3043319b66ff74770bcbacd962a31740bc9a7aa9bca6c
readcube_id
Levermore
David
Springer Nature - SN SciGraph project
Claude
Bardos
10.1007/bf01026608
doi
University of Arizona
Departement of Mathematics, University of Arizona, 85721, Tucson, Arizona