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DISCRETE AND CONTINUOUS doi:10.3934/dcds.2011.29.xx DYNAMICAL SYSTEMS
 

Summary: DISCRETE AND CONTINUOUS doi:10.3934/dcds.2011.29.xx
DYNAMICAL SYSTEMS
Volume 29, Number 3, March 2011 pp. 1­XX
SOLVABILITY OF THE FREE BOUNDARY VALUE PROBLEM
OF THE NAVIER-STOKES EQUATIONS
Hantaek Bae
Center For Scientific Computation And Mathematical Modeling
University of Maryland
4125 CSIC Building, Paint Branch Drive
College Park, MD 20742, USA
(Communicated by Fanghua Lin)
Abstract. In this paper, we study the incompressible Navier-Stokes equations
on a moving domain in R3 of finite depth, bounded above by the free surface
and bounded below by a solid flat bottom. We prove that there exists a unique,
global-in-time solution to the problem provided that the initial velocity field
and the initial profile of the boundary are sufficiently small in Sobolev spaces.
1. Introduction. In this paper, we study a viscous free boundary value problem
with surface tension. The Navier-Stokes equations describe the evolution of the
velocity field in the fluid body. With boundary conditions stated below, we have
the following system of equations:

  

Source: Anisimov, Mikhail - Institute for Physical Science and Technology & Department of Chemical Engineering and Biomolecular Engineering, University of Maryland at College Park

 

Collections: Physics; Materials Science