Existence de nappes de tourbillon en dimension deux

Existence de nappes de tourbillon en dimension deux
HTML articles powered by AMS MathViewer

J. Amer. Math. Soc. 4 (1991), 553-586

DOI: https://doi.org/10.1090/S0894-0347-1991-1102579-6

PDF | Request permission

References

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, DOI 10.1007/978-1-4612-1029-0

Un phénomène de concentration évanescente pour des flots nonstationnaires incompressibles en dimension deux

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, DOI 10.1007/BF01239528
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, DOI 10.1002/cpa.3160400304
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, DOI 10.1090/S0894-0347-1988-0924702-6
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 271984, DOI 10.2307/1970699
V. Georgescu, Some boundary value problems for differential forms on compact Riemannian manifolds, Ann. Mat. Pura Appl. (4) 122 (1979), 159–198. MR 565068, DOI 10.1007/BF02411693
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, DOI 10.1002/cpa.3160410303
Tosio Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188–200. MR 211057, DOI 10.1007/BF00251588

Non-stationary plane flow of viscous and ideal fluids

27

Variétés différentiables

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
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, DOI 10.1017/S0022112086002732

Computation of vortex sheet roll-up in the Trefftz plane

184

Andrew Majda, Vortex dynamics: numerical analysis, scientific computing, and mathematical theory, ICIAM ’87: Proceedings of the First International Conference on Industrial and Applied Mathematics (Paris, 1987) SIAM, Philadelphia, PA, 1988, pp. 153–182. MR 976858

The interaction of nonlinear analysis and modern applied mathematics