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arXiv · 1707.03096

Global solvability of the Navier-Stokes equations with a free surface in the maximal $L_p\text{-}L_q$ regularity class

Hirokazu Saito
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Abstract

We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the $N$-dimensional Euclidean space for $N\geq 2$ when the gravity is not taken into account. The aim of this paper is to show the global solvability of the Naiver-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal $L_p\text{-}L_q$ regularity class. Our approach is based on the maximal $L_p\text{-}L_q$ regularity with exponential stability for the linearized equations, and solutions to the original nonlinear problem are also exponentially stable.

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Hirokazu Saito. 2017-07-27. Global solvability of the Navier-Stokes equations with a free surface in the maximal $L_p\text{-}L_q$ regularity class. https://arxiv.org/abs/1707.03096

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