Hilbert expansion of the Boltzmann equation with specular boundary condition in half-space

Abstract

Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. Based on a systematic derivation and study of the viscous layer equations and the $L^2$ to $L^{\infty }$ framework, we establish the validity of the Hilbert expansion for the Boltzmann equation with specular reflection boundary conditions, which leads to derivations of compressible Euler equations and acoustic equations.

arXiv comment65 pages, comments are welcome

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Cited by in corpus (7)

• Recent developments in mathematical aspects of relativistic fluids
• Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space
• Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition
• Kinetic-fluid boundary layers and acoustic limit for the Boltzmann equation with general Maxwell reflection boundary condition
• Grad-Caflisch pointwise decay estimates revisited
• Stability of Rarefaction Waves for the Non-cutoff Vlasov-Poisson-Boltzmann System with Physical Boundary
• On the Cauchy problem of the Boltzmann equation with a very soft potential