Communications on Pure and Applied Mathematics · 2003 · 138 citations · 11 references
Boundary ConditionsBoltzmann EquationEngineeringPhysicsBounded DomainPotential TheoryFluid MechanicsStokes‐fourier SystemFree Boundary ProblemNonlinear Hyperbolic ProblemRenormalized SolutionsBoltzmann Transport Equation
Abstract We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes‐Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a bounded domain. © 2003 Wiley Periodicals, Inc.
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