Maximal regularity for a free boundary problem

authored by

Joachim Escher, Gieri Simonett

Abstract

This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law. We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.

External Organisation(s)

University of Basel
Vanderbilt University

Type

Article

Journal

Nonlinear Differential Equations and Applications NoDEA

Volume

2

Pages

463-510

No. of pages

48

ISSN

1021-9722

Publication date

12.1995

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Applied Mathematics

Electronic version(s)

https://doi.org/10.1007/BF01210620 (Access: Unknown)