On the non-uniqueness of weak solution of the Euler equations

A. Shnirelman

Journées équations aux dérivées partielles (1996)

  • Volume: 1996, page 1-10
  • ISSN: 0752-0360

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Shnirelman, A.. "On the non-uniqueness of weak solution of the Euler equations." Journées équations aux dérivées partielles 1996 (1996): 1-10. <http://eudml.org/doc/93325>.

@article{Shnirelman1996,
author = {Shnirelman, A.},
journal = {Journées équations aux dérivées partielles},
keywords = {non-constant kinetic energy; two-dimensional torus; discontinuous unbounded weak solution; incompressible homogeneous Euler equations; compact support in time; inverse energy cascade; two-dimensional turbulence theory},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {On the non-uniqueness of weak solution of the Euler equations},
url = {http://eudml.org/doc/93325},
volume = {1996},
year = {1996},
}

TY - JOUR
AU - Shnirelman, A.
TI - On the non-uniqueness of weak solution of the Euler equations
JO - Journées équations aux dérivées partielles
PY - 1996
PB - Ecole polytechnique
VL - 1996
SP - 1
EP - 10
LA - eng
KW - non-constant kinetic energy; two-dimensional torus; discontinuous unbounded weak solution; incompressible homogeneous Euler equations; compact support in time; inverse energy cascade; two-dimensional turbulence theory
UR - http://eudml.org/doc/93325
ER -

References

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  1. [CET] P. Constantin, W. E., E. Titi, Onsager's conjecture on the energy conservation for solutions of the Euler's equations. Communications of Mathematical Physics 165 (1994) 207-209. Zbl0818.35085MR96e:76025
  2. [D] J.-M. Delort, Existence des nappes de tourbillon en dimension deux. Journal of the American Mathematical Society 4(3) (1991) 553-586. Zbl0780.35073MR92f:76019
  3. [E] G.L. Eyink, Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer. Physica D. 78(3-4) (1994) 222-240. Zbl0817.76011MR95m:76020
  4. [K] R.H. Kraichnan, Inertial ranges in two-dimensional turbulence. Physics of Fluids 10(7) (1967) 1417-1423. 
  5. [O] L. Onsager, Statistical hydrodynamics. Nuovo Cimento (Supplemento) 6 (1949) 279. MR12,60f
  6. [S] V. Scheffer, An inviscid flow with compact support in space-time. Journal of Geometric Analysis 3(4) (1993) 343-401. Zbl0836.76017MR94h:35215

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