# American Institute of Mathematical Sciences

2011, 2011(Special): 437-446. doi: 10.3934/proc.2011.2011.437

## Variational inequality for the Stokes equations with constraint

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

Received  June 2010 Revised  February 2011 Published  October 2011

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.
Citation: Takeshi Fukao. Variational inequality for the Stokes equations with constraint. Conference Publications, 2011, 2011 (Special) : 437-446. doi: 10.3934/proc.2011.2011.437
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