On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

M. Pulvirenti

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 1, page 265-274
  • ISSN: 0392-4041

Abstract

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This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.

How to cite

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Pulvirenti, M.. "On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 265-274. <http://eudml.org/doc/290464>.

@article{Pulvirenti2008,
abstract = {This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.},
author = {Pulvirenti, M.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {265-274},
publisher = {Unione Matematica Italiana},
title = {On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation},
url = {http://eudml.org/doc/290464},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Pulvirenti, M.
TI - On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 265
EP - 274
AB - This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.
LA - eng
UR - http://eudml.org/doc/290464
ER -

References

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  1. BLANCHET, A. - DOLBEAULT, J. - PERTHAME, B., Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions. Electron. J. Differential Equations, No. 44 (electronic) (2006), 32. Zbl1112.35023MR2226917
  2. CAGLIOTI, E. - LIONS, P.-L. - MARCHIORO, C. - PULVIRENTI, M., A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Comm. Math. Phys., 143, 3 (1992), 501-525. Zbl0745.76001MR1145596
  3. CAGLIOTI, E. - LIONS, P.-L. - MARCHIORO, C. - PULVIRENTI, M., A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. II. Comm. Math. Phys., 174, 2 (1995), 229-260. Zbl0840.76002MR1362165
  4. CAGLIOTI, E. - PULVIRENTI, M. - ROUSSET, F., Quasistationary states for the 2-D Navier-Stokes Equation. preprint (2007). 
  5. CAGLIOTI, E. - PULVIRENTI, M. - ROUSSET, F., 2-D constrained Navier-Stokes Equation and intermediate asymptotic. preprint (2007). Zbl1143.76022MR2456338DOI10.1088/1751-8113/41/34/344001
  6. GOGNY, D. - LIONS, P. L., Sur les états d'èquilibre pour les densitès électroniques dans les plasmas. RAIRO Modèl Math. Anal. Num., 23, no. 1 (1989), 137-153. Zbl0665.76145MR1015923DOI10.1051/m2an/1989230101371
  7. JAGER, W. - LUCKHAUS, S., On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc., 329, no. 2 (1992), 819-824. Zbl0746.35002MR1046835DOI10.2307/2153966
  8. M. KIESSLING, K.-H., Statistical mechanics of classical particles with logarithmic interactions. Comm. Pure Appl. Math., 46, no. 1 (1993), 27-56. Zbl0811.76002MR1193342DOI10.1002/cpa.3160460103
  9. M. KIESSLING, K.-H. - LEBOWITZ, J. L., The micro-canonical point vortex ensemble: beyond equivalence. Lett. Math. Phys., 42, no. 1 (1997), 43-58. Zbl0902.76021MR1473359DOI10.1023/A:1007370621385
  10. LUNGREN, T. S. - POINTIN, Y. B., Statistical mechanics of two-dimensional vortices in a bounded container. Phys. Fluids, 19 (1976), 1459-1470. Zbl0339.76013
  11. MARCHIORO, C. - PULVIRENTI, M., Mathematical Theory of Incompressible Nonviscous Fluids. Appl Math series, n. 96Springer (1991). Zbl0789.76002MR1245492DOI10.1007/978-1-4612-4284-0
  12. MONTGOMERY, D. - JOYCE, G., Statistical mechanics of "negative temperature" states. Phys. Fluids, 17 (1974), 1139-1145. MR384035DOI10.1063/1.1694856
  13. ONSAGER, L., Statistical hydrodynamics. Nuovo Cimento (9) 6, Supplemento, 2 (Convegno Internazionale di Meccanica Statistica) (1949), 279-287. MR36116

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