On the nonuniqueness of weak solution of the Euler equation

Communications on Pure and Applied Mathematics

Volumn 50, Issue 12, 1997, Pages 1261-1286

  Shnirelman, A ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031491102     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199712)50:12<1261::AID-CPA3>3.0.CO;2-6     Document Type: Article

References (9)

1. Constantin, P., E, W., and Titi, E. S., Onsager's conjecture on the energy conservation for solutions of the Euler's equation, Comm. Math. Phys. 165, 1994, pp. 207-209.
2. Delort, J.-M., Existence des nappes de tourbillon en dimension deux, J. Amer. Math. Soc. 4(3), 1991, pp. 553-586.
3. Ebin, D. G., and Marsden, J., Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92, 1970, pp. 102-163.
4. Eyink, G. L., Energy dissipation without viscosity in ideal hydrodynamics I: Fourier analysis and local energy transfer, Phys. D 78(3-4), 1994, pp. 222-240.
5. Hörmander, L., Pseudo-differential operators, Comm. Pure Appl. Math. 18, 1965, pp. 501-517.
6. Kraichnan, R. H., Inertial ranges in two-dimensional turbulence, Phys. Fluids 10(7), 1967, pp. 1417-1423.
7. Onsager, L., Statistical hydrodynamics, Nuovo Cimento (9) Supplemente No. 2 (Convegno Internazionale di Meccanica Statistica), 6, 1949, pp. 279-287.
8. Scheffer, V., An inviscid flow with compact support in space-time, J. Geom. Anal. 3(4), 1993, pp. 343-401.
9. Shnirelman, A., Weak solutions of incompressible Euler equations with decreasing energy, C. R. Acad. Sci. Paris Sér. I Math., 1997, to appear.