Convergence of a vector BGK approximation for the incompressible Navier-Stokes equations
Analysis of PDEs
2019-12-10 v2
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.
Keywords
Cite
@article{arxiv.1705.04026,
title = {Convergence of a vector BGK approximation for the incompressible Navier-Stokes equations},
author = {Roberta Bianchini and Roberto Natalini},
journal= {arXiv preprint arXiv:1705.04026},
year = {2019}
}