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Consider the resolvent problem associated with the linearized viscous flowaround a rotating body. Within a setting of classical Sobolev spaces, thisproblem is not well posed on the whole imaginary axis. Therefore, a frameworkof homogeneous Sobolev spaces is introduced where existence of a uniquesolution can be guaranteed for every purely imaginary resolvent parameter. Forthis purpose, the problem is reduced to an auxiliary problem, which is studiedby means of Fourier analytic tools in a group setting. In the end, uniformresolvent estimates can be derived, which lead to the existence of solutions tothe associated time-periodic linear problem.

On the Stokes-type resolvent problem associated with time-periodic flow around a rotating obstacle