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Research talks;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 ...
37K10 ; 35C07 ; 35C08 ; 35Q53 ; 35Q55 ; 76B15 ; 76Fxx
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Research talks;Partial Differential Equations
The Euler-Korteweg system corresponds to compressible, inviscid fluids with capillary forces. It can be used to model diffuse interfaces. Mathematically it reads as the Euler equations with a third order dispersive perturbation corresponding to the capillary tensor.
In dimension one there exists traveling waves with equal or different limit at infinity, respectively solitons and kinks. Their stability is ruled by a simple criterion a la Grillakis-Shatah-Strauss. This talk is devoted to the construction of multiple traveling waves, namely global solutions that converge as $t\rightarrow \infty $ to a profile made of several (stable) traveling waves. The waves constructed have both solitons and kinks. Multiple traveling waves play a peculiar role in the dynamics of dispersive equations, as they correspond to solutions that follow in some sense a purely nonlinear evolution.
The Euler-Korteweg system corresponds to compressible, inviscid fluids with capillary forces. It can be used to model diffuse interfaces. Mathematically it reads as the Euler equations with a third order dispersive perturbation corresponding to the capillary tensor.
In dimension one there exists traveling waves with equal or different limit at infinity, respectively solitons and kinks. Their stability is ruled by a simple criterion a la ...
35Q35 ; 35C07 ; 35Q53 ; 35Q31 ; 35B35
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- xiv; 419 p.
ISBN 978-3-03719-197-2
Series of congress reports
Localisation : Ouvrage RdC (SPEC)
distribution universelle # probabilité libre # processus de Markov # opérateur de Schrödinger # noyau thermique # écologie spatiale # métastabilité # analyse numérique # régularité critique # ordre apériodique # système dynamique # structure spéciale de Kähler # partitions non croisées # sous-catégorie de localisation # fonction zêta # croissance des sous-groupes # croissance des représentations # conjecture de Brumer-Stark # groupe p-divisible
58J65 ; 52C23 ; 20F65 ; 11M41 ; 46L54 ; 60J45 ; 35C07 ; 35Q55 ; 43A25 ; 20F36 ; 11R42 ; 14L05
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