Local Hilbert expansion for the Boltzmann equation

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March 2009, 2(1): 205-214. doi: 10.3934/krm.2009.2.205

Local Hilbert expansion for the Boltzmann equation

Yan Guo ^1, , Juhi Jang ^2, and Ning Jiang ^2,

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

Received September 2008 Revised October 2008 Published January 2009

Abstract
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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: Boltzmann equations., fluid dynamic limit.

Mathematics Subject Classification: Primary: 76P05, 35L67; Secondary: 82A4.

Citation: Yan Guo, Juhi Jang, Ning Jiang. Local Hilbert expansion for the Boltzmann equation. Kinetic & Related Models, 2009, 2 (1) : 205-214. doi: 10.3934/krm.2009.2.205

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