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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.

76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
Full Text: DOI
[1] [Dri88] Dritschel, D.G.: Nonlinear Stability Bounds for Inviscid, Two-Dimensional, Parallel or Circular Flows with Monotonic vorticity, and Analogous Three-dimensional Quasi-Geostrophis Flows. J. Fluid Mech.191, 575–581 (1988) · Zbl 0643.76059 · doi:10.1017/S0022112088001715
[2] [Dri89] Dritschel, D.G.: Contour Dynamics and Contour Surgery: Numerical Algorithms for Extended, High-Resolution Modelling of Vortex Dynamics in Two-Dimensional, Inviscid, Incompressible Flows. Computer Phys. Reports10, 77–146 (1989) · doi:10.1016/0167-7977(89)90004-X
[3] [Lam32] Lamb, H.: Hydrodynamics, 6. ed. Cambridge: Cambridge University Press, 1932
[4] [Mar88] Marchioro, C.: Euler Evolution for Singular Initial Data and Vortex Theory: A Global Solution. Commun. Math. Phys.116, 45–55 (1988) · Zbl 0654.76017 · doi:10.1007/BF01239024
[5] [Ma85] Marchioro, C., Pulvirenti, M.: Some Considerations on the Nonlinear Stability of Stationary Planar Euler Flows. Commun. Math. Phys.100, 343–354 (1985) · Zbl 0625.76060 · doi:10.1007/BF01206135
[6] [Ma92] Marchioro, C., Pulvirenti, M.: Vortices and localization in Euler flows. Commun. Math. Phys.154, 49–61 (1993) · Zbl 0774.35058 · doi:10.1007/BF02096831
[7] [MaP94] Marchioro, C., Pulvirenti, M.: Mathematical theory of incompressible nonviscous fluids. Applied Mathematical Sciences 96, Berlin, Heidelberg, New York: Springer 1994 · Zbl 0789.76002
[8] [WaP85] Wan, Y.H., Pulvirenti, M.: Nonlinear Stabilityof Circular Vortex Patch. Commun. Math. Phys.99, 435–450 (1985) · Zbl 0584.76062 · doi:10.1007/BF01240356
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