Translator Disclaimer
2005 The initial-value problem for the Navier-Stokes equations with a free surface in $L^q$-Sobolev spaces
Helmut Abels
Adv. Differential Equations 10(1): 45-64 (2005).

Abstract

We prove small-time existence of strong solutions of a free-boundary-value problem, which describes the motion of an incompressible viscous fluid occupying a semi-infinite domain bounded above by a free surface. This problem was studied by Beale [6] and others in $L^2$-Sobolev spaces. In contrast to the latter contribution we study solutions in $L^q$-Sobolev spaces for $q>n$ in space dimension $n\geq 2$. This approach has the advantage that the regularity assumptions can be reduced in comparison to [6]. In order to solve the linearized system, we use the nonstationary reduced Stokes equations with a mixed boundary condition and the maximal regularity of the associated reduced Stokes operator.

Citation

Download Citation

Helmut Abels. "The initial-value problem for the Navier-Stokes equations with a free surface in $L^q$-Sobolev spaces." Adv. Differential Equations 10 (1) 45 - 64, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1105.35072
MathSciNet: MR2106120

Subjects:
Primary: 35Q30
Secondary: 35R35, 76D03, 76D05

Rights: Copyright © 2005 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.10 • No. 1 • 2005
Back to Top