Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle
Tom 70 / 2005
Streszczenie
Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space $\mathbb R^3$. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper {Far} the author proved $L^q$-estimates of second order derivatives uniformly in the angular and translational velocities, $\omega$ and $k$, of the obstacle, whereas the transport terms fails to have $L^q$-estimates independent of $\omega$. In this paper we clarify this unexpected behavior and prove weighted $L^q$-estimates of first order terms independent of $\omega$.
