Relaxed Euler systems and convergence to Navier-Stokes equations

Abstract We consider the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation both in compressible and incompressible cases. This requires to decompose second-order derivative terms velocity into first-order ones. Usual decompositions lead approximate tensor variables. construct vector variables using Hurwitz-Radon matrices. These are written form balance laws admit strictly convex entropies, so that they symmetrizable hyperbolic. For smooth solutions, we prove convergence uniform time intervals. Global-in-time is also shown initial data near constant equilibrium states systems. results established not only but those