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arXiv · 1705.04026

Convergence of a vector BGK approximation for the incompressible Navier-Stokes equations

Roberta Bianchini·Roberto Natalini
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Abstract

We present a rigorous convergence result for the smooth solutions to a singular semilinear hyperbolic approximation, a vector BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof is based on the use of a constant right symmetrizer, weighted with respect to the parameter of the singular pertubation system. This symmetrizer provides a conservative-dissipative form for the system and this allow us to perform uniform energy estimates and to get the convergence by compactness.

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Roberta Bianchini, Roberto Natalini. 2017-05-11. Convergence of a vector BGK approximation for the incompressible Navier-Stokes equations. https://arxiv.org/abs/1705.04026

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