Dissipative continuous Euler flows

Inventiones Mathematicae

Volumn 193, Issue 2, 2013, Pages 377-407

  de Lellis, Camillo ^a   Székelyhidi Jr , László ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881551330     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-012-0429-9     Document Type: Article

References (28)

1. Chiodaroli, E.: A counterexample to well-posedness of entropy solutions to the incompressible Euler system. Preprint (2012).
2. Constantin, P., Majda, A.: The Beltrami spectrum for incompressible fluid flows. Commun. Math. Phys. 115(3), 435-456 (1988).
3. Constantin, P. E. W., Titi, E. S.: Onsager's conjecture on the energy conservation for solutions of Euler's equation. Commun. Math. Phys. 165(1), 207-209 (1994).
4. 1,α isometric embeddings. In: Proceedings of the Abel Symposia, vol. 7, pp. 83-116 (2012). doi: 10. 1007/978-3-642-25361-4_5.
5. Cordoba, D., Faraco, D., Gancedo, F.: Lack of uniqueness for weak solutions of the incompressible porous media equation. Arch. Ration. Mech. Anal. 200(3), 725-746 (2011).
6. De Lellis, C., Székelyhidi, L. Jr.: The Euler equations as a differential inclusion. Ann. Math. (2) 170(3), 1417-1436 (2009).
7. De Lellis, C., Székelyhidi, L. Jr.: On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195(1), 225-260 (2010).
8. De Lellis, C., Székelyhidi, L. Jr.: The h-principle and the equations of fluid dynamics. Preprint (2011).
9. Duke, W.: An introduction to the Linnik problems. In: Equidistribution in Number Theory, an Introduction. NATO Sci. Ser. II Math. Phys. Chem., vol. 237, pp. 197-216. Springer, Dordrecht (2007).
10. Eliashberg, Y., Mishachev, N.: Introduction to the h-principle. Graduate Studies in Mathematics, vol. 48. American Mathematical Society, Providence (2002).
11. Eyink, G. L.: Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer. Physica D 78(3-4), 222-240 (1994).
12. Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001). Reprint of the 1998 edition.
13. Gromov, M.: Partial Differential Relations. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 9. Springer, Berlin (1986).
14. Iwaniec, H.: Fourier coefficients of modular forms of half-integral weight. Invent. Math. 87(2), 385-401 (1987).
15. Kirchheim, B., Müller, S., Šverák, V.: Studying nonlinear PDE by geometry in matrix space. In: Hildebrandt, S., Karcher, H. (eds.) Geometric Analysis and Nonlinear Partial Differential Equations, pp. 347-395. Springer, Berlin (2003).
16. Linnik, Y. V.: Ergodic Properties of Algebraic Fields. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 45. Springer, New York (1968). Translated from the Russian by M. S. Keane.
17. 1 isometric imbeddings. Ann. Math. 60, 383-396 (1954).
18. Onsager, L.: Statistical hydrodynamics. Nuovo Cimento (9) 6(Suppl. 2), 279-287 (1949). (Convegno Internazionale di Meccanica Statistica).
19. Sarnak, P.: Some Applications of Modular Forms. Cambridge Tracts in Mathematics, vol. 99. Cambridge University Press, Cambridge (1990).
20. Scheffer, V.: An inviscid flow with compact support in space-time. J. Geom. Anal. 3(4), 343-401 (1993).
21. Shnirelman, A.: On the nonuniqueness of weak solution of the Euler equation. Commun. Pure Appl. Math. 50(12), 1261-1286 (1997).
22. Shnirelman, A.: Weak solutions with decreasing energy of incompressible Euler equations. Commun. Math. Phys. 210(3), 541-603 (2000).
23. Shvydkoy, R.: Convex integration for a class of active scalar equations. J. Am. Math. Soc. 24(4), 1159-1174 (2011).
24. Simon, L.: Schauder estimates by scaling. Calc. Var. Partial Differ. Equ. 5(5), 391-407 (1997).
25. Sychev, M. A.: A few remarks on differential inclusions. Proc. R. Soc. Edinb., Sect. A 136(3), 649-668 (2006).
26. Székelyhidi, L. Jr.: Relaxation of the incompressible porous medium equation. Ann. Sci. l'ENS 45(3), 491-509 (2012).
27. Székelyhidi, L. Jr., Wiedemann, E.: Young measures generated by ideal incompressible fluid flows. doi: 10. 1007/s00205-012-0540-5.
28. Wiedemann, E.: Existence of weak solutions for the incompressible Euler equations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28(5), 727-730 (2011).