Global existence for hyperbolic Navier–Stokes equations in Gevrey class

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Abstract In this paper, we consider a hyperbolic perturbation of the 2D Navier–Stokes equations, which consists in adding the term ε ⁢ u t ⁢ t {\varepsilon u_{tt}} to the Navier–Stokes equations. We prove the global persistence of analyticity and Gevrey-class of solutions. Moreover, we prove that the solution to the perturbed Navier–Stokes equations approximates the solution to the classical Navier–Stokes equations.