The Stokes Limit for the Boltzmann
نویسندگان
چکیده
The Stokes equations are the linearization of the incompressible Navier-Stokes equations about zero. They may be derived directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. The present paper establishes this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have uctuations that converge entropically (and hence strongly in L 1) to a unique limit governed by a solution of the Stokes equations for all time, provided that its initial uctuations converge entropically to an appropriate limit associated to any given L 2 initial data of the Stokes equations. Local momentum conservation is recovered in the limit.
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