An Extension Of Marchioro's Bound On The Growth Of A Vortex Patch To Flows With Lp Vorticity

We observe that C. Marchioro's cubic-root bound in time on the growth of the diameter of a patch of vorticity [Comm. Math. Phys, 164 (1994), pp. 507-524] can be extended to incompressible two-dimensional Euler flows with compactly supported initial vorticity in Lp, p > 2, and with a distinguished sign.293596599Delort, J.-M., Existence de nappes de tourbillons en dimension deux (1991) J. Amer. Math. Soc., 4, pp. 553-586Majda, A., Vorticity and the mathematical theory of incompressible fluid flow (1986) Comm. Pure Appl. Math., 39, pp. S187-S220Marchioro, C., Bounds on the growth of the support of a vortex patch (1994) Comm. Math. Phys., 164, pp. 507-524Schocket, S., The weak vorticity formulation of the 2D Euler equations and concentration-cancellation (1995) Comm. Partial Differential Equations, 20, pp. 1077-110