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An Extension of Marchioro's Bound on the Growth of a Vortex Patch to Flows with series\itshape L$^\mbox\scriptsizeseries\itshapep$ Vorticity

1998; Society for Industrial and Applied Mathematics; Volume: 29; Issue: 3 Linguagem: Inglês

10.1137/s0036141096310910

1095-7154

Milton C. Lopes Filho, Milton C. Lopes Filho,

Computational Fluid Dynamics and Aerodynamics

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.