Weak solutions of incompressible Euler equations with decreasing energy

Alexander I. Shnirelman[1]

  • [1] School of Mathematical Sciences, Tel-Aviv University, and IHES

Séminaire Équations aux dérivées partielles (1996-1997)

  • Volume: 326, Issue: 3, page 1-9

How to cite

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Shnirelman, Alexander I.. "Weak solutions of incompressible Euler equations with decreasing energy." Séminaire Équations aux dérivées partielles 326.3 (1996-1997): 1-9. <http://eudml.org/doc/10920>.

@article{Shnirelman1996-1997,
affiliation = {School of Mathematical Sciences, Tel-Aviv University, and IHES},
author = {Shnirelman, Alexander I.},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {weak solution of incompressible Euler equations; turbulent fluid motion at high Reynolds numbers; generalized flows},
language = {eng},
number = {3},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Weak solutions of incompressible Euler equations with decreasing energy},
url = {http://eudml.org/doc/10920},
volume = {326},
year = {1996-1997},
}

TY - JOUR
AU - Shnirelman, Alexander I.
TI - Weak solutions of incompressible Euler equations with decreasing energy
JO - Séminaire Équations aux dérivées partielles
PY - 1996-1997
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 326
IS - 3
SP - 1
EP - 9
LA - eng
KW - weak solution of incompressible Euler equations; turbulent fluid motion at high Reynolds numbers; generalized flows
UR - http://eudml.org/doc/10920
ER -

References

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  1. Y. Brenier, The Least Action Principle and the related concept of generalized flows for incompressible perfect fluids. J. Amer. Math Soc., 2:2 (1989). Zbl0697.76030MR969419
  2. Y. Brenier, A dual Least Action Principle for the motion of an ideal incompressible fluid. Arch. Rat. Mech. Anal., v.122 (1993), no. 4, 323-351. Zbl0797.76006MR1217592
  3. P. Constantin, W. E, E. Titi, Onsager’s conjecture on the energy conservation for the solutions of the Euler equations. Comm. Math. Phys., v.165 (1994), 207-209. Zbl0818.35085
  4. G. Eyink, Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer. Physica D, v. 78 (1994), no. 3-4, 222-240. Zbl0817.76011MR1302409
  5. L. Onsager, Statistical hydromechanics. Nuovo Cimento (Supplemento), v.6 (1949), 279. MR36116
  6. V. Scheffer, An inviscid flow with compact support in space-time. J. Geom. Anal., v.3 (1993), no. 4, 343-401. Zbl0836.76017MR1231007
  7. A. Shnirelman, On the geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid. Math. USSR Sbornik, v. 56 (1987), no. 1, 79-105. Zbl0725.58005
  8. A. Shnirelman, Generalized fluid flows, their approximation and applications. Geom. And Funct. Anal., v.4 (1994), no. 5, 586-620. Zbl0851.76003MR1296569
  9. A.Shnirelman, On the non-uniqueness of weak solution of the Euler equations. Preprint IHES, 1996. See also Journees “Equations aux Derivees Partielles” (Saint-Jean-de-Monts, 1996), Exp. No. XVIII, Ecole Polytechnic, Palaiseau, 1996. Zbl0881.35096

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