## On the growth of the vorticity support for an incompressible non-viscous fluid in a two-dimensional exterior domain.(English)Zbl 0845.35089

Summary: We study the time evolution of the support of a positive vorticity for a non-viscous incompressible fluid evolving in $$\mathbb{R}^2- D$$, where $$D$$ is a compact domain with smooth boundary. We bound its growth. In the same time we prove also that a fluid particle initially close to the origin cannot go fast away.

### MSC:

 35Q35 PDEs in connection with fluid mechanics 35Q05 Euler-Poisson-Darboux equations 76B47 Vortex flows for incompressible inviscid fluids
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### References:

 [1] Dritschel, J. Fluid Mech. 191 pp 575– (1988) · Zbl 0643.76059 [2] Dritschel, Comput. Phys. Reports 10 pp 77– (1989) [3] Marchioro, Commun. Math. Phys. 100 pp 343– (1985) · Zbl 0625.76060 [4] and , Mathematical Theory of Incompressible Nonviscous Fluids, Applied Mathematical Sciences, Vol. 96, Springer, New York, 1994. · Zbl 0789.76002 [5] Marchioro, Commun. Math. Phys. 164 pp 507– (1994) · Zbl 0839.76010 [6] Wan, Commun. Math. Phys. 99 pp 435– (1985) · Zbl 0584.76062
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