On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body

Jiří Neustupa

doi:10.3934/proc.2007.2007.758

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2007, Volume 2007: 758-767. Doi: 10.3934/proc.2007.2007.758 open access

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On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body

Jiří Neustupa^1,

1.
Mathematical Institute of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1

Received: September 2006

Revised: January 2007

Published: August 2007

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Abstract

We deal with a $C_0$–semigroup generated by the linearized problem for perturbations of a flow of an incompressible viscous fluid around a rotating body. Although the uniform growth bound of the semigroup is non–negative, we derive a sufficient condition for the uniform boundedness of the semigroup.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 35Q35, 47D60, 76D07.

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