Variational inequality for the Stokes equations with constraint

Takeshi Fukao

doi:10.3934/proc.2011.2011.437

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2011, Volume 2011: 437-446. Doi: 10.3934/proc.2011.2011.437 open access

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Variational inequality for the Stokes equations with constraint

Takeshi Fukao^1,

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

Received: May 31, 2010

Revised: January 31, 2011

Published: August 2017

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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 subdierential 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 subdierential and obtain suitable limit conditions.

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Mathematics Subject Classification: Primary: 35K86, 35Q35; Secondary: 76D07.

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