Abstract
We present a rigorous convergence result for smooth solutions to a singular semilinear hyperbolic approximation, called vector-BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof deeply relies on the dissipative properties of the system and on the use of an energy which is provided by a symmetrizer, whose entries are weighted in a suitable way with respect to the singular perturbation parameter. This strategy allows us to perform uniform energy estimates and to prove the convergence by compactness.
Anno
2019
Autori IAC
Tipo pubblicazione
Altri Autori
Bianchini, Roberta; Natalini, Roberto
Editore
American Institute of Mathematical Sciences
Rivista
Kinetic & related models