Local Hilbert expansion for the Boltzmann equation

Yan Guo; Juhi Jang; Ning Jiang

doi:10.3934/krm.2009.2.205

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2009, Volume 2, Issue 1: 205-214. Doi: 10.3934/krm.2009.2.205

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Local Hilbert expansion for the Boltzmann equation

1.
Brown University, Providence, RI 02912
2.
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York City, NY 10012

Received: August 31, 2008

Revised: September 30, 2008

Published: February 2009

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Abstract

We revisit the classical work of Caflisch [1] for compressible Euler limit of the Boltzmann equation. By using a new $L^{2}\mbox{-}L^{\infty }$ method, we prove the validity of the Hilbert expansion before shock formations in the Euler system with moderate temperature variation.

Keywords:

fluid dynamic limit,
Boltzmann equations.

Mathematics Subject Classification: Primary: 76P05, 35L67; Secondary: 82A40.

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