On Nonperiodic Euler Flows with Hölder Regularity

Archive for Rational Mechanics and Analysis

Volumn 221, Issue 2, 2016, Pages 725-804

  Isett, Philip ^a   Oh, Sung Jin ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84959133509     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-016-0973-3     Document Type: Article

References (30)

1. Buckmaster, T., De Lellis, C., Isett, P., Székelyhidi Jr., L.: Anomalous dissipation for 1/5-Hölder Euler flows. Ann. Math. (2)182(1), 127–172 (2015)
2. Buckmaster, T. De Lellis, C., Székelyhidi Jr., L.: Transporting microstructures and dissipative Euler flows (2013, preprint)
3. Buckmaster, T., De Lellis, C., Székelyhidi Jr., L.: Dissipative Euler flows with Onsager-critical spatial regularity (2014, preprint)
4. Bogovskii M.E.: Solution for some vector analysis problems connected with operators div and grad, theory of cubature formulas and application of functional analysis to problems of mathematical physics. Trudy Sem. SL Soboley 1, 5–40 (1980)
5. Buckmaster T.: Onsager’s conjecture almost everywhere in time. Commun. Math. Phys. 333(3), 1175–1198 (2015)
6. Cheskidov A., Constantin P., Friedlander S., Shvydkoy R.: Energy conservation and Onsager’s conjecture for the Euler equations. Nonlinearity 21(6), 1233–1252 (2008)
7. Constantin P., Weinan E., Titi E.S.: Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Commun. Math. Phys. 165(1), 207–209 (1994)
8. Choffrut A.: h-Principles for the incompressible Euler equations. Arch. Rational Mech. Anal. 210(1), 133–163 (2013)
9. Cheskidov, A., Shvydkoy, R.: Euler equations and turbulence: analytical approach to intermittency (2012, preprint)
10. Choffrut, A., Székelyhidi Jr., L.: Weak solutions to the stationary incompressible Euler equations (2014, preprint)
11. De Lellis C., Székelyhidi L. Jr.: On admissibility criteria for weak solutions of the Euler equations. Arch. Rational Mech. Anal. 195(1), 225–260 (2010)
12. De Lellis, C., Székelyhidi Jr., L.: Dissipative Euler flows and Onsager’s conjecture (2012, preprint)
13. De Lellis C., Székelyhidi L. Jr.: The h-principle and the equations of fluid dynamics. Bull. Am. Math. Soc. (N.S.) 49(3), 347–375 (2012)
14. De Lellis C., Székelyhidi L.: Dissipative continuous Euler flows. Invent. Math. 193(2), 377–407 (2013)
15. De Lellis C., Székelyhidi L. Jr.: Dissipative Euler flows and Onsager’s conjecture. J. Eur. Math. Soc. (JEMS) 16(7), 1467–1505 (2014)
16. Duchon J., Robert R.: Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations. Nonlinearity 13(1), 249–255 (2000)
17. Eyink, G.L., Sreenivasan, K.R.: Onsager and the theory of hydrodynamic turbulence. Rev. Modern Phys. 78 (2006)
18. Eyink G.L.: Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer. Phys. D 78(3–4), 222–240 (1994)
19. Eyink G.L.: Dissipative anomalies in singular Euler flows. Phys. D 237(14–17), 1956–1968 (2008)
20. Frisch U., Sulem P.-L.: A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87(4), 719–736 (1978)
21. Isett, P., Oh, S.-J.: A heat flow approach to Onsager’s conjecture for the Euler equations on manifolds. Trans. Amer. Math. Soc.368(9), 6519–6537 (2016)
22. Isett, P., Oh, S.-J.: On the kinetic energy profile of Hölder continuous Euler flows (2015, preprint)
23. Isett, P.: Hölder continuous Euler flows in three dimensions with compact support in time (2012, preprint)
24. Isett, P.: Regularity in time along the coarse scale flow for the Euler equations (2013, preprint)
25. Isett, P., Vicol, V.: Holder continuous solutions of active scalar equations (2014, preprint)
26. Kolmogorov A.N.: The local structure of turbulence in an incompressible viscous fluid. C. R. (Doklady) Acad. Sci. URSS (N.S.) 30, 301–305 (1941)
27. Onsager L.: Statistical hydrodynamics. Nuovo Cimento (9), Convegno Internazionale di Meccanica Statistica. 6(Suppl 2), 279–287 (1949)
28. Oh, S.-J., Tataru, D.: Local well-posedness of the (4+1)-dimensional Maxwell–Klein–Gordon equation at energy regularity (2015, preprint)
29. Shvydkoy, R.: Lectures on the Onsager conjecture. Discrete Contin. Dyn. Syst. Ser. S 33, 473–496
30. Taylor, M.E.: Partial differential equations I. Basic theory, 2nd edn. Applied Mathematical Sciences, Vol. 115. Springer, New York (2011)