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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

Pages: 758 - 767, Issue Special, September 2007

 Abstract        Full Text (233.0K)              

Jiří Neustupa - Mathematical Institute of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic (email)

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.

Keywords:  Stability, C_0–semigroups, modified Oseen operator, rotating obstacle.
Mathematics Subject Classification:  Primary: 35Q30; Secondary: 35Q35, 47D60, 76D07.

Received: September 2006;      Revised: January 2007;      Published: September 2007.