Obiettivo The research will be focused on the analytical dynamics of an in viscid incompressible fluid. This is the area, which development is going on permanently (mention the classical results by V.I.Arnold J.E.Marsden D.Ebin T. Ratiu, P. Constantin, P.D. Lax, J. Gibbon, B. Khesin, V.E. Zakharov et al.) . Further progress of analytical fluid dynamics provides the decisive tools for advances in the central problems on the Euler equations which still remain unsolved, albeit only their solution provides a base for the theories of vanishing viscosity and developed turbulence. We mean the global existence and uniqueness theorems 3D both for smooth and for weak solutions, the stability problem for 3D flows, the problems of long time behavior of vortex structures, the applications of the liberalization approaches etc. Usual way to study a conservative system (as an ideal fluid in an impermeable container) is to identify all possible integrals (conservation laws) and then study the dynamics of the Routh-type equations on the joint level surfaces of those integrals. If the considered system is subjected to constrains, then additional principal and technical difficulties appear even in the simplest case of holonomic and stationary constrains. In studying the dynamics of in viscid incompressible fluid we have to deal with such the situation. Now we have the results on Routh-type equations, and strongly hope to decide the crucial questions : whether the dynamics of ideal fluid is of regular, or chaotic, or of mixed regular-chaotic type. It is well known that the violation of the fundamental conservation laws creates the main obstacles in investigation of the long time behavior of dynamical systems, for instance of vortex structures in a fluid. In the Routh equations all the conservation laws are satisfied automatically. We propose to develop the reductions (in Routh sense) on joint level surfaces of vorticity integrals and constraints for ideal fluid together with the theory of Poisson and generalized Poisson systems (the last ones are not subjected to the Jacobi's identity) as a tool for all the issues below. We plan to derive and to study the Routh-type equations of fluid dynamics, that include the Kirchoff equations of point vortices as a limiting case. We plan to apply the above general approach to the several concrete problems in the dynamics and control of vortex structures (discrete and continual) , including numerical simulations and experimental verification of the employed mathematical models. Among the tasks are: the invertiblity problem for Arnolds stability criterion, qualitative topological analysis of dynamics of discrete vortex configurations, nonlinear stability problems for permanent rotations and translations of discrete and continual configurations of vortices (including stratified fluid), and further development of the theory of stability and oscillations for in viscid flows through a prescribed domain. Parole chiave Flows through a given domain New methods of analytical dynamics Point and continuous vortex structures Programma(i) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Argomento(i) Airbus 2004 - INTAS Collaborative Call with Airbus Invito a presentare proposte Data not available Meccanismo di finanziamento NoE - Network of Excellence Coordinatore Universite de Bretagne Occidentale Contributo UE Nessun dato Indirizzo Avenue le Gorgeu 6 29200 Brest Francia Mostra sulla mappa Costo totale Nessun dato Partecipanti (7) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto CNRS Francia Contributo UE Nessun dato Indirizzo rue de la Piscine 1025 38041 Grenoble Mostra sulla mappa Costo totale Nessun dato Eindhoven University of Technology Paesi Bassi Contributo UE Nessun dato Indirizzo Den Dolech 2 5600 Eindhoven Mostra sulla mappa Costo totale Nessun dato Institute of Computer Science Russia Contributo UE Nessun dato Indirizzo Universitetskaya 1 426034 Izhevsk Mostra sulla mappa Costo totale Nessun dato Kiev National Taras Shevchenko University Ucraina Contributo UE Nessun dato Indirizzo Volodymyrska 64 01033 Kiev Mostra sulla mappa Costo totale Nessun dato POLITECNICO DI TORINO Italia Contributo UE Nessun dato Indirizzo CORSO DUCA DEGLI ABRUZZI, 24 TORINO Mostra sulla mappa Costo totale Nessun dato Rostov State University Russia Contributo UE Nessun dato Indirizzo Zorge 5 344090 Rostov-on-Don Mostra sulla mappa Costo totale Nessun dato UNIVERSITY OF YORK Regno Unito Contributo UE Nessun dato Indirizzo HESLINGTON YORK Mostra sulla mappa Costo totale Nessun dato
