Abstract
We study the behavior of a quasi-geostrophic flow in thef-plane. We consider a positive initial potential vorticity with a compact support and we bound the growth in time of its support. We prove also that a fluid particle cannot go fast away from the initial position.
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Bertozzi, A. L. and Constantin, P.,Global regularity for vortex patches, Commun. Math. Phys.152, 19–23 (1993).
Chemin, J. Y.,Persistance de structure géometriques dans les fluides incompressibles bidimensionnels, Ann. Scient. Ec. Norm. Sup.26, 517–542 (1993).
Dritschel, D. G.,Nonlinear stability bounds for inviscid two-dimensional, parallel or circular flows with monotonic vorticity, and analogous three-dimensional quasi-geostrophic flows, J. Fluid Mech.191, 575–581 (1988).
Marchioro, C. and Pulvirenti, M.,Some considerations on the nonlinear stability of the stationary planar Euler flows, Commun. Math. Phys.100, 343–354 (1985).
Marchioro, C. and Pulvirenti, M.,Mathematical Theory of Incompressible Nonviscous Fluids, Appl. Math. Sci.96, Springer Verlag, New York 1994.
Marchioro, C.,Bounds on the growth of the support of a vortex patch, Commun. Math. Phys.164, 507–524 (1994).
Marchioro, C.,On the growth of the vorticity support for an incompressible nonviscous fluid in a two-dimensional exterior domain, Math. Meth. Appl. Sci. (1995) (in press).
Pedlosky, J.,Geophysical Fluid Dynamics. Springer-Verlag, New York, Heidelberg, Berlin 1979.
Wan, Y. H. and Pulvirenti, M.,Nonlinear stability of circular vortex patch, Commun. Math. Phys.99, 435–450 (1985).
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Marchioro, C. A confinement result on a quasi-geostrophic flow in thef-plane. Z. angew. Math. Phys. 47, 16–27 (1996). https://doi.org/10.1007/BF00917571
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DOI: https://doi.org/10.1007/BF00917571