Global solvability of the Navier-Stokes equations with a free surface in the maximal L-p-L-q regularity class

摘要

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 >= 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 L-p-L-q regularity class. Our approach is based on the maximal L-p-L-q regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable. (c) 2017 Elsevier Inc. All rights reserved.