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arXiv · 2111.13052

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

Nacer Aarach
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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.

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Nacer Aarach. 2021-11-25. Global well-posedness of 2D Hyperbolic perturbation of the Navier-Stokes system in a thin strip. https://arxiv.org/abs/2111.13052

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