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Bounds on the growth of the support of a vortex path. (English) Zbl 0839.76010
Summary: We study the time evolution of the support of a vortex patch evolving in \(\mathbb{R}^2\) according to the Euler equation for an incompressible fluid and we bound its growth. Furthermore, we discuss the same problem in the framework of a simplified model. Finally, we consider a similar problem for the Navier-Stokes flow.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
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