Global well-posedness of 2D Hyperbolic perturbation of the Navier–Stokes system in a thin strip

Abstract

In this paper, we study a hyperbolic version of the Navier–Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl type equation, our goal is to prove the existence and uniqueness of a global solution to these equations for analytic initial data in the tangential variable, under a uniform smallness assumption. Then we justify the limit from the anisotropic hyperbolic Navier–Stokes system to the hydrostatic hyperbolic Navier–Stokes system with small analytic data.