On boundary-driven time-dependent Oseen flows. (English) Zbl 1148.76016

Rencławowicz, Joanna (ed.) et al., Parabolic and Navier-Stokes equations. Part 1. Proceedings of the confererence, Bȩdlewo, Poland, September 10–17, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 81, Pt. 1, 119-132 (2008).
Summary: We consider the single-layer potential associated to the fundamental solution of time-dependent Oseen system. It is shown this potential belongs to \(L^2 (0,\infty,H^1 (\Omega)^3)\) and to \(H^1 (0,\infty,V')\) if the layer function is in \(L^2 (\partial\Omega \times (0,\infty)^3)\). (\(\Omega\) denotes the complement of a bounded Lipschitz set; \(V\) denotes the set of smooth solenoidal functions in \(H^1_0 (\Omega)^3\).) This result means that the usual weak solution of time-dependent Oseen function with zero initial data and zero body force may be represented by a single-layer potential, provided a certain integral equation involving the boundary data may be solved.
For the entire collection see [Zbl 1147.35005].


76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics
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