The properties of the solutions of the incompressible flows on an exterior domain

In this paper, we want to see the properties of the smooth solutions u of the incompressible flows on an exterior domain Ω of R2. Specially, when the vorticity ω=∇×u has a bounded support, with suitable conditions we will show that there exists a constant C(p,q) such that ∥u∥Lp(Ω)≤C∥u∥Lq(Ω) for 1