Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898992 | Journal of Differential Equations | 2018 | 46 Pages |
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 Nâ¥2. The aim of this paper is to show the global solvability of the Navier-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal Lp-Lq regularity class. Our approach is based on the maximal Lp-Lq regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hirokazu Saito,