Variational inequality for the Stokes equations with constraint

Pages: 437 - 446, Issue Special, September 2011

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Takeshi Fukao - Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522, Japan (email)

Abstract: In this paper, the existence problem of the variational inequality for the constrained Stokes equations is considered, in 2- and 3-dimensions with bounded domain. The evolution equation is governed by the subdi erential which formulates the pointwise constraint by the time-dependent obstacle functions. Thanks to the penalty method due to Temam, the hindrance of divergence freeness is avoided. We then characterize the Yosida approximation of the subdi erential and obtain suitable limit conditions.

Keywords:  Stokes equations, obstacle problem, pointwise constraint
Mathematics Subject Classification:  Primary: 35K86, 35Q35; Secondary: 76D07

Received: June 2010;      Revised: February 2011;      Published: October 2011.