# American Institute of Mathematical Sciences

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

## Local Hilbert expansion for the Boltzmann equation

 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

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