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July, 2011 A non-autonomous model problem for the Oseen-Navier-Stokes flow with rotating effects
Matthias GEISSERT, Tobias HANSEL
J. Math. Soc. Japan 63(3): 1027-1037 (July, 2011). DOI: 10.2969/jmsj/06331027


Consider the Navier-Stokes flow past a rotating obstacle with a general time-dependent angular velocity and a time-dependent outflow condition at infinity. After rewriting the problem on a fixed domain, one obtains a non-autonomous system of equations with unbounded drift terms. It is shown that the solution to a model problem in the whole space case Rd is governed by a strongly continuous evolution system on Lpσ(Rd) for 1 < p < ∞. The strategy is to derive a representation formula, similar to the one known in the case of non-autonomous Ornstein-Uhlenbeck equations. This explicit formula allows to prove Lp-Lq estimates and gradient estimates for the evolution system. These results are key ingredients to obtain (local) mild solutions to the full nonlinear problem by a version of Kato's iteration scheme.


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Matthias GEISSERT. Tobias HANSEL. "A non-autonomous model problem for the Oseen-Navier-Stokes flow with rotating effects." J. Math. Soc. Japan 63 (3) 1027 - 1037, July, 2011.


Published: July, 2011
First available in Project Euclid: 1 August 2011

zbMATH: 1229.35178
MathSciNet: MR2836754
Digital Object Identifier: 10.2969/jmsj/06331027

Primary: 35Q30
Secondary: 76D03 , 76D05

Keywords: Navier-Stokes flow , non-autonomous PDE , Oseen flow , rotating obstacle

Rights: Copyright © 2011 Mathematical Society of Japan


Vol.63 • No. 3 • July, 2011
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