Compactness of the gain parts of the linearized       Boltzmann operator with weakly cutoff kernels

C. David Levermore; Weiran Sun

doi:10.3934/krm.2010.3.335

Article Contents

2010, Volume 3, Issue 2: 335-351. Doi: 10.3934/krm.2010.3.335

This issue Previous Article Analytical and numerical investigations of refined macroscopic traffic flow models Next Article Fluid modeling for the Knudsen compressor: Case of polyatomic gases

Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels

C. David Levermore^1, and
Weiran Sun^2,

1.
Department of Mathematics & Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
2.
Department of Mathematics, University of Maryland, College Park, MD 20742

Received: August 31, 2009

Revised: October 31, 2009

Published: May 2010

Abstract Related Papers Cited by

Abstract

We prove an $L^p$ compactness result for the gain parts of the linearized Boltzmann collision operator associated with weakly cutoff collision kernels that derive from a power-law intermolecular potential. We replace the Grad cutoff assumption previously made by Caflisch [1], Golse and Poupaud [7], and Guo [11] with a weaker local integrability assumption. This class includes all classical kernels to which the DiPerna-Lions theory applies that derive from a repulsive inverse-power intermolecular potential. In particular, our approach allows the treatment of both hard and soft potential cases.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

Article Metrics

HTML views() PDF downloads(79) Cited by(0)

Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content