Kračmar, Stanislav; Nečasová, Šárka; Penel, Patrick \(L^q\)-approach to weak solutions of the Oseen flow around a rotating body. (English) Zbl 1148.76017 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, 259-276 (2008). Summary: We consider time-periodic Oseen flow around a rotating body in \({\mathbb R}^3\). We prove a priori estimates in \(L^q\)-spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates, the problem is reduced to a stationary Oseen equation with the additional term \(-(\omega \wedge x) \cdot \nabla u + \omega \wedge u\) in the equation of momentum, where \(\omega\) denotes the angular velocity. We prove the existence of generalized weak solutions in \(L^q\)-space using Littlewood-Paley decomposition and maximal operators.For the entire collection see [Zbl 1147.35005]. Cited in 6 Documents MSC: 76D07 Stokes and related (Oseen, etc.) flows 76U05 General theory of rotating fluids 35Q35 PDEs in connection with fluid mechanics Keywords:Bogovskii operator; existence; Littlewood-Paley decomposition PDFBibTeX XMLCite \textit{S. Kračmar} et al., Banach Cent. Publ. 81, 259--276 (2008; Zbl 1148.76017) Full Text: Link