$L^{q}$-approach of weak solutions to stationary rotating Oseen equations in exterior domains
Authors:
S. Kračmar, Š. Nečasová 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
Full-text PDF Free Access
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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, Nečasov á, 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. Kračmar
Affiliation:
Department of Technical Mathematics, FS ČVUT, Czech Technical University, Karlovo n ám. 13, 12135 Prague 2, Czech Republic
Email:
Stanislav.Kracmar@fs.cvut.cz
Š. Nečasová
Affiliation:
Mathematical Institute of Academy of Sciences, Žitn á 25, 11567 Prague 1, Czech Republic
MR Author ID:
306796
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
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