A Representation Formula for the Velocity Part of 3D Time-Dependent Oseen Flows

We prove a representation formula for the solution of an initial-boundary value problem associated with the 3D time-dependent Oseen system. This formula involves the solution of an integral equation on the lateral boundary of the space-time cylinder. The key point of this article is that the assumpt...

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Bibliographic Details
Published in:Journal of mathematical fluid mechanics 2014-03, Vol.16 (1), p.1-39
Main Author: Deuring, Paul
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
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Summary:We prove a representation formula for the solution of an initial-boundary value problem associated with the 3D time-dependent Oseen system. This formula involves the solution of an integral equation on the lateral boundary of the space-time cylinder. The key point of this article is that the assumptions on the data are chosen in such a way that the formula in question may be used in a theory of the asymptotic behaviour of solutions to the nonstationary 3D Navier–Stokes system with Oseen term (incompressible viscous flow in an exterior domain with nonzero velocity at infinity).
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-013-0134-5