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

Kračmar, S.; Nečasová, Š.; Penel, P.

doi:10.1090/S0033-569X-10-01210-4

$L^{q}$-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
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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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