Consider the incompressible 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 $U(t,s)$ on $L^p_\sigma(\Omega)$ for $1<p<\infty$. Moreover, $L^p-L^q$ smoothing properties and gradient estimates of $U(t,s)$ are obtained. These results are the key ingredients to show local in time existence of mild solutions to the full nonlinear problem for initial value in $L^p_\sigma(\Omega), p\ge d$.
The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous case
RHANDI, Abdelaziz
2014-01-01
Abstract
Consider the incompressible 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 $U(t,s)$ on $L^p_\sigma(\Omega)$ for $1I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
