Vector-BGK approximation to fluid-dynamics equations.

A singular semilinear hyperbolic approximation to the Euler and the incompressible Navier-Stokes equations, inspired by the kinetic theory, is considered. In the first part of the talk, I will illustrate the structure of this approximation. Then, I will present a result of convergence of the vector-BGK to the 2D incompressible Navier-Stokes equations under the diffusive scaling.