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Partial Differential Equations;Mathematical Physics

In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed in the talk. In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed ...

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Documents 76Fxx | enregistrements trouvés : 57

Unresolved problems in the theory of integrable systems Zakharov, Vladimir | CIRM H Nouveau

Fluid dynamicsproceedings of the 4th. symposium in applied mathematics of the a.m.s. held at the university of maryland,june 22-23,1951 Martin, M. H. | American Mathematical Society 1953 Nouveau

Applied probabilityproceedings of the 7th symposium in applied mathematics of the a.m.s. held at the polytechnic instituts of brooklyn,april 14-15,1955 Maccoll, L. A. | American Mathematical Society 1957 Nouveau

Transition and turbulenceproceedings of a symposium conducted by the Mathematics Research CenterUniversity of WisconsinOct. 13-15 Meyer, Richard E. | Academic Press 1981 Nouveau

Dynamics and processes :proceedings of the 3rd encounter in mathematics and physics held in bielefeld#Nov. 30 - Dec. 4 Blanchard, Ph. ; Streit, L. | Springer-Verlag 1983 Nouveau

Chaos and statistical methodsproceedings of the sixth kyoto summer institute,kyoto,japan,sept. 12-15,1983 Kuramoto, Y. | Springer-Verlag 1984 Nouveau

Turbulence models and their applications. Vol. 2 :cours donnnés à la 22ème session Ecole d'Ete d'analyse numérique#CEA, EDF, INRIA#Juillet 15-30 Launder, B. E ; Reynolds, W. C. ; Rodi, W. | Editions Eyrolles 1984 Nouveau

Theoretical approaches to turbulenceformal workshop held in hampton,oct. 10-12,1984 Dwoyer, D. L. ; Hussaini, M. Y. ; Voigt, R. G. | Springer-Verlag 1985 Nouveau

Turbulence and diffusion in stable environmentsproceedings of a conference on... in stably stratified regions of the natural environment held in cambridge, march,1983 Hunt, J. C. R. | Clarendon Press 1985 Nouveau

Vortex methodsproceedings of the u.c.l.a. workshop,held in los angeles,may 20-22,1987 Anderson, C. ; Greengard, C. | Springer-Verlag 1988 Nouveau

Multigrid methods iiiproceedings of papers presented at the third european conference on...Oct. 1-4 Hackbusch, W. ; Trottenberg, U. | Birkhäuser Verlag 1991 Nouveau

Nonlinear analysis and microlocal analysisproceedings of the international conference at Nankai institute of mathematics Tianjin, China18-23 August Chang, Kung-Ching ; Huang, Yu-Min ; Li, Ta-Tsien | World Scientific 1992 Nouveau

Statistical mechanics and dynamical systemsand papers from the 1976 Duke turbulence conference Ruelle, David | Mathematics department Duke University 1977 Nouveau

Colloque sur les rythmes en biologie, chimie, physique et autres champs d'applicationsLuminySept. 14-18 Cosnard, M. ; Demongeot, J. ; Le Breton, A. | S.N. 1981 Nouveau

Scale invariance and beyondworkshopMarch 10-14 Dubrulle, B. ; Graner, F. ; Sornette, D. | EDP Sciences;Springer 1997 Nouveau

Numerical methods in fluid mechanics Vincent, Alain | American Mathematical Society 1998 Nouveau

Séminaire Bourbaki. Vol. 1982/83 :exposés 597-614 | Société Mathématique de France 1983 Nouveau

The mechanics of turbulence.Proceedings of the conferenceMarseille # august 28 - september 2, 1961 | Gordon and Breach Sciences Publishers 1964 Nouveau

Mécanique de la turbulence.Colloque international du CNRSMarseille # 28 août - 2 septembre 1961 Favre, Alexandre | Editions du Centre National de la Recherche Scientifique 1962 Nouveau

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Fluid dynamics
proceedings of the 4th. symposium in applied mathematics of the a.m.s. held at the university of maryland,june 22-23,1951 Martin, M. H. | American Mathematical Society 1953 Nouveau

Applied probability
proceedings of the 7th symposium in applied mathematics of the a.m.s. held at the polytechnic instituts of brooklyn,april 14-15,1955 Maccoll, L. A. | American Mathematical Society 1957 Nouveau

Transition and turbulence
proceedings of a symposium conducted by the Mathematics Research Center
University of Wisconsin
Oct. 13-15 Meyer, Richard E. | Academic Press 1981 Nouveau

Dynamics and processes :
proceedings of the 3rd encounter in mathematics and physics held in bielefeld#Nov. 30 - Dec. 4 Blanchard, Ph. ; Streit, L. | Springer-Verlag 1983 Nouveau

Chaos and statistical methods
proceedings of the sixth kyoto summer institute,kyoto,japan,sept. 12-15,1983 Kuramoto, Y. | Springer-Verlag 1984 Nouveau

Turbulence models and their applications. Vol. 2 :
cours donnnés à la 22ème session Ecole d'Ete d'analyse numérique#CEA, EDF, INRIA#Juillet 15-30 Launder, B. E ; Reynolds, W. C. ; Rodi, W. | Editions Eyrolles 1984 Nouveau

Theoretical approaches to turbulence
formal workshop held in hampton,oct. 10-12,1984 Dwoyer, D. L. ; Hussaini, M. Y. ; Voigt, R. G. | Springer-Verlag 1985 Nouveau

Turbulence and diffusion in stable environments
proceedings of a conference on... in stably stratified regions of the natural environment held in cambridge, march,1983 Hunt, J. C. R. | Clarendon Press 1985 Nouveau

Vortex methods
proceedings of the u.c.l.a. workshop,held in los angeles,may 20-22,1987 Anderson, C. ; Greengard, C. | Springer-Verlag 1988 Nouveau

Multigrid methods iii
proceedings of papers presented at the third european conference on...
Oct. 1-4 Hackbusch, W. ; Trottenberg, U. | Birkhäuser Verlag 1991 Nouveau

Nonlinear analysis and microlocal analysis
proceedings of the international conference at Nankai institute of mathematics
Tianjin, China
18-23 August Chang, Kung-Ching ; Huang, Yu-Min ; Li, Ta-Tsien | World Scientific 1992 Nouveau

Statistical mechanics and dynamical systems
and papers from the 1976 Duke turbulence conference Ruelle, David | Mathematics department Duke University 1977 Nouveau

Colloque sur les rythmes en biologie, chimie, physique et autres champs d'applications
Luminy
Sept. 14-18 Cosnard, M. ; Demongeot, J. ; Le Breton, A. | S.N. 1981 Nouveau

Scale invariance and beyond
workshop
March 10-14 Dubrulle, B. ; Graner, F. ; Sornette, D. | EDP Sciences;Springer 1997 Nouveau

Séminaire Bourbaki. Vol. 1982/83 :
exposés 597-614 | Société Mathématique de France 1983 Nouveau

The mechanics of turbulence.
Proceedings of the conference
Marseille # august 28 - september 2, 1961 | Gordon and Breach Sciences Publishers 1964 Nouveau

Mécanique de la turbulence.
Colloque international du CNRS
Marseille # 28 août - 2 septembre 1961 Favre, Alexandre | Editions du Centre National de la Recherche Scientifique 1962 Nouveau