Asymptotic Properties Of The Vorticity Of Incompressible Flows

We investigate the confinement properties of bounded, nonnegative, com-pactly supported vortices of axisymmtric Euler flows without swirl. We showthat along one direction of the symmetry axis, its support can grow no fasterthan O[(tlogt)^1/2]. Also, the distance from a fluid particle to the axis at timet, r(t), is at least r(O)e^-Ct. These results are complementary to the result ofMaffei-Marchioro on the rate of growth of the support in the radial direction.This thesis is divided into four chapters. In chapter 1, we introduce theproblem and state our results. In chapter 2, notations, needed formulas andresults are quoted. In chapter 3, we prove our results. We conclude with chapter4 and indicate some directions for future investigations.