Time-dependent obstacle problem in thermohydraulics

Pages: 240 - 249, Issue Special, September 2009

 Abstract        Full Text (173.2K)              

Takeshi Fukao - Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522, Japan (email)
Masahiro Kubo - Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan (email)

Abstract: Obstacle problems, mathematical models of some nonlinear phenomena accompanying a free boundary, have been well studied. In this paper, the existence and uniqueness of a system between the obstacle problem and the Navier-Stokes equations is considered. The abstract theory for evolution equations governed by a subdifferential of the indicator functional on a time-dependent, closed, and convex set is applied to show the main theorem. $L^\infty $-estimate is an important lemma to prove the existence theorem.

Keywords:  Variational inequality, Obstacle problem, Navier-Stokes equations
Mathematics Subject Classification:  Primary: 35K65, 76D05; Secondary: 35G3

Received: July 2008;      Revised: February 2009;      Published: September 2009.