$L^p$-stability estimates for the spatially inhomogeneous discrete
velocity Boltzmann model
Seung-Yeal Ha - Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea (email)
Abstract: 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.
Keywords: The discrete velocity Boltzmann model, nonlinear functional, $L^p$ stability, macro-micro decomposition
Received: December 2007; Revised: June 2008; Published: December 2008.
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