English

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}
}