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2009, 2009(Special): 240-249. doi: 10.3934/proc.2009.2009.240

Time-dependent obstacle problem in thermohydraulics

Takeshi Fukao 1, and  Masahiro Kubo 2,

1. 

Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522, Japan
2. 

Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555

Received  July 2008 Revised  February 2009 Published  September 2009

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, Navier-Stokes equations, Obstacle problem.
Mathematics Subject Classification: Primary: 35K65, 76D05; Secondary: 35G3.
Citation: Takeshi Fukao, Masahiro Kubo. Time-dependent obstacle problem in thermohydraulics. Conference Publications, 2009, 2009 (Special) : 240-249. doi: 10.3934/proc.2009.2009.240
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