Hyperbolic quasilinear Navier-Stokes equations in \({\mathbb{R}}^2\)
A hyperbolic correction to the Navier-Stokes equations reflects the application of the Cattaneo law instead of the usual Fourier approximation, and lead to avoiding infinite speed phenomena. The authors analyze two-dimensional hyperbolic version of these equations, and show local-in-time existence of solutions. Moreover, global-in-time results are derived under some smallness assumptions. Those assumptions disappear in the limit of vanishing hyperbolic correction to the classical Navier-Stokes equation recovering their well-known global-in-time solvability in two-dimensional setting.
scientific article; zbMATH DE number 7616284