$L^q$-approach to weak solutions of the Oseen flow around a rotating body
Tom 81 / 2008
Banach Center Publications 81 (2008), 259-276
MSC: Primary 76D05; Secondary 35Q30.
DOI: 10.4064/bc81-0-17
Streszczenie
We consider the time-periodic Oseen flow around a rotating body in $\mathbb R^{3}$. We prove a priori estimates in $L^{q}$-spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term $-(\omega\wedge x)\cdot\nabla u+\omega\wedge u$ in the equation of momentum where $\omega$ denotes the angular velocity. We prove the existence of generalized weak solutions in $L^{q}$-space using Littlewood-Paley decomposition and maximal operators.
