Existence de nappes de tourbillon en dimension deux

Delort, Jean-Marc

doi:10.1090/S0894-0347-1991-1102579-6

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Existence de nappes de tourbillon en dimension deux

Author: Jean-Marc Delort
Journal: J. Amer. Math. Soc. 4 (1991), 553-586
MSC: Primary 76C05; Secondary 35Q30
MathSciNet review: 1102579
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[1] R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, tensor analysis, and applications, 2nd ed., Applied Mathematical Sciences, vol. 75, Springer-Verlag, New York, 1988. MR 960687 (89f:58001)
[2] S. Alinhac, Un phénomène de concentration évanescente pour des flots nonstationnaires incompressibles en dimension deux, Prépublications de l'Université Paris-Sud.
[3] J.-Y. Chemin, Sur le mouvement des particules d’un fluide parfait incompressible bidimensionnel, Invent. Math. 103 (1991), no. 3, 599–629 (French). MR 1091620 (91m:35187), http://dx.doi.org/10.1007/BF01239528
[4] Ronald J. DiPerna and Andrew J. Majda, Concentrations in regularizations for 2-D incompressible flow, Comm. Pure Appl. Math. 40 (1987), no. 3, 301–345. MR 882068 (88e:35149), http://dx.doi.org/10.1002/cpa.3160400304
[5] Ronald J. DiPerna and Andrew Majda, Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow, J. Amer. Math. Soc. 1 (1988), no. 1, 59–95. MR 924702 (89e:35126), http://dx.doi.org/10.1090/S0894-0347-1988-0924702-6
[6] David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid., Ann. of Math. (2) 92 (1970), 102–163. MR 0271984 (42 #6865)
[7] V. Georgescu, Some boundary value problems for differential forms on compact Riemannian manifolds, Ann. Mat. Pura Appl. (4) 122 (1979), 159–198. MR 565068 (81d:58053), http://dx.doi.org/10.1007/BF02411693
[8] Claude Greengard and Enrique Thomann, On DiPerna-Majda concentration sets for two-dimensional incompressible flow, Comm. Pure Appl. Math. 41 (1988), no. 3, 295–303. MR 929281 (89d:35141), http://dx.doi.org/10.1002/cpa.3160410303
[9] Tosio Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188–200. MR 0211057 (35 #1939)
[10] F. Mac Grath, Non-stationary plane flow of viscous and ideal fluids, Arch. Rational Mech. Anal. 27 (1968), 328-348.
[11] G. de Rham, Variétés différentiables, Hermann, Actualités Sci. Indust., Paris, 1960.
[12] Yu Xi Zheng, Concentration-cancellation for the velocity fields in two-dimensional incompressible fluid flows, Comm. Math. Phys. 135 (1991), no. 3, 581–594. MR 1091579 (92e:35131)
[13] Robert Krasny, A study of singularity formation in a vortex sheet by the point-vortex approximation, J. Fluid Mech. 167 (1986), 65–93. MR 851670 (87g:76028), http://dx.doi.org/10.1017/S0022112086002732
[14] -, Computation of vortex sheet roll-up in the Trefftz plane, J. Fluid Mech. 184 (1987), 123-155.
[15] Andrew Majda, Vortex dynamics: numerical analysis, scientific computing, and mathematical theory, Industrial and Applied Mathematics (Paris, 1987) SIAM, Philadelphia, PA, 1988, pp. 153–182. MR 976858 (90f:65227)
[16] -, The interaction of nonlinear analysis and modern applied mathematics, Proc. I.C.M., Kyoto (à paraître).

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