Regularity properties of a generalized Oseen evolution operator in exterior domains, with applications to the Navier-Stokes initial value problem

Abstract

Consider a generalized Oseen evolution operator in 3D exterior domains, that is generated by a non-autonomous linearized system arising from time-dependent rigid motions. This was found by Hansel and Rhandi, and then the theory was developed by the second author, however, desired regularity properties such as estimate of the temporal derivative as well as the Hoelder estimate have remained open. The present paper provides us with those properties together with weighted estimates of the evolution operator. The results are then applied to the Navier-Stokes initial value problem, so that a new theorem on existence of a unique strong Lq-solution locally in time is proved.

arXiv comment49 pages, Corrected typos

References in corpus (4)

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• On the Navier-Stokes equations with rotating effect and prescribed outflow velocity
• Stability of time-dependent motions for fluid-rigid ball interaction
• Spatial pointwise behavior of time-periodic Navier-Stokes flow induced by oscillation of a moving obstacle