Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



$ L^{q}$-approach of weak solutions to stationary rotating Oseen equations in exterior domains

Authors: S. Kracmar, S. Necasová and P. Penel
Journal: Quart. Appl. Math. 68 (2010), 421-437
MSC (2000): Primary 76D05; Secondary 35Q30, 35Q35
DOI: https://doi.org/10.1090/S0033-569X-10-01210-4
Published electronically: May 6, 2010
MathSciNet review: 2676969
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Abstract: We establish the existence and uniqueness of a weak solution of the three-dimensional nonhomogeneous stationary Oseen flow around a rotating body in an exterior domain $ D$. We mainly use the localization procedure (see Kozono and Sohr (1991)) to combine our previous results (see Kračmar, Nečasová , and Penel (2007, 2008)) with classical results in an appropriate bounded domain. We study the case of a nonintegrable right-hand side, where $ f$ is given in $ (\widehat{W}^{-1,q}(D))^3$ for certain values of $ q$.

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Additional Information

S. Kracmar
Affiliation: Department of Technical Mathematics, FS ČVUT, Czech Technical University, Karlovo n am. 13, 12135 Prague 2, Czech Republic
Email: Stanislav.Kracmar@fs.cvut.cz

S. Necasová
Affiliation: Mathematical Institute of Academy of Sciences, Žitn a 25, 11567 Prague 1, Czech Republic
Email: matus@math.cas.cz

P. Penel
Affiliation: University of Sud, Toulon–Var, Department of Mathematics and Laboratory S.N.C., B.P. 20132, 83957 La Garde Cedex, France
Email: penel@univ-tln.fr

DOI: https://doi.org/10.1090/S0033-569X-10-01210-4
Keywords: Rotating body, stationary Oseen flow, weak solution, $L^q$ approach, exterior domain
Received by editor(s): February 8, 2008
Published electronically: May 6, 2010
Article copyright: © Copyright 2010 Brown University

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