Abstract
In this paper, we want to see the properties of the smooth solutions u of the incompressible flows on an exterior domain Ω of R 2 . 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 ∥ L p ( Ω ) ≤ C ∥ u ∥ L q ( Ω ) for 1 < p ≤ q ≤ ∞ .
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