The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous case

Details The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous case The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous case

2010-06-18

arxiv.org/abs/1006.3643v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

Consider the Navier-Stokes flow past a rotating obstacle with a general time-dependent angular velocity and a time-dependent outflow condition at infinity -- sometimes called an Oseen condition. By a suitable change of coordinates the problem is transformed to an non-autonomous problem with unbounded drift terms on a fixed exterior domain $\Omega\subset \R^d$. It is shown that the solution to the linearized problem is governed by a strongly continuous evolution system $\{T_\Omega(t,s)\}_{t\geq s\geq0}$ on $L^p_\sigma(\Omega)$ for $1

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