# American Institute of Mathematical Sciences

March  2009, 11(2): 353-364. doi: 10.3934/dcdsb.2009.11.353

## $L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model

 1 Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea 2 Department of Mathematics and Computer Science, International Christian University, Tokyo 181-8585, Japan

Received  December 2007 Revised  June 2008 Published  December 2008

We present two a priori $L^p$-stability estimates to the discrete velocity Boltzmann models. In a close-to-global Maxwellian regime, we derive a local-in-time $L^2$-stability estimate using a macro-micro decomposition and dispersion estimates for smooth perturbations, and as a direct application, we establish that classical solutions in Kawashima's framework [22, 24] are uniformly $L^2$-stable. In a close-to-vacuum regime, we also obtain a local-in-time $L^p$-stability estimates for classical solutions near vacuum.
Citation: Seung-Yeal Ha, Mitsuru Yamazaki. $L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 353-364. doi: 10.3934/dcdsb.2009.11.353
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