Rigorous results and conjectures on stationary space-periodic 2D turbulence

Sergei B. Kuksin

Séminaire Équations aux dérivées partielles (2006-2007)

  • Volume: 2006-2007, page 1-16

Abstract

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We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.

How to cite

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Kuksin, Sergei B.. "Rigorous results and conjectures on stationary space-periodic 2D turbulence." Séminaire Équations aux dérivées partielles 2006-2007 (2006-2007): 1-16. <http://eudml.org/doc/11163>.

@article{Kuksin2006-2007,
abstract = {We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.},
author = {Kuksin, Sergei B.},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Navier-Stokes equation; periodic boundary conditions; turbulence; vorticity; Eulerian limit},
language = {eng},
pages = {1-16},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Rigorous results and conjectures on stationary space-periodic 2D turbulence},
url = {http://eudml.org/doc/11163},
volume = {2006-2007},
year = {2006-2007},
}

TY - JOUR
AU - Kuksin, Sergei B.
TI - Rigorous results and conjectures on stationary space-periodic 2D turbulence
JO - Séminaire Équations aux dérivées partielles
PY - 2006-2007
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2006-2007
SP - 1
EP - 16
AB - We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.
LA - eng
KW - Navier-Stokes equation; periodic boundary conditions; turbulence; vorticity; Eulerian limit
UR - http://eudml.org/doc/11163
ER -

References

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  11. —, Randomly Forced Nonlinear PDEs and Statistical Hydrodynamics in 2 Space Dimensions, Europear Mathematical Society Publishing House, 2006, also see mp_arc 06-178. Zbl1099.35083MR2225710
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  13. —, Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model, preprint, see mp _ arc 07-25 (2007). 
  14. —, On distribution of energy and vorticity for solutions of 2D Navier-Stokes equations with small viscosity, preprint, see mp _ arc 07-60 (2007). 
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  16. K. R. Parthasarathy, Introduction to Probability and Measure, Macmillan, 1977. Zbl0395.28001MR651012

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