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

  • * Corresponding author: Roberto Natalini

    * Corresponding author: Roberto Natalini
The first author was supported by a Ph. D. grant of University of Rome Tor Vergata.
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  • 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.

    Mathematics Subject Classification: Primary: 35Q35, 35Q30; Secondary: 75M45, 35L40.


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