ROGER TEMAM, Indiana University Bloomington THE ATMOSPHERE-ICES-OCEAN SYSTEMS. ITS COMPLEXITY, ITS MODELING
Workshop: Mathematics in a Complex World
on the occasion of 150th year of Politecnico di Milano Giovedì 28 Febbraio 2013, ore 17:45 Politecnico di Milano | |
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PAOLO CASCINI, Imperial College, London CURVE RAZIONALI IN GEOMETRIA ALGEBRICA Lunedì 04 Febbraio 2013, ore 17:00 Dipartimento di Matematica, Università di Milano, Via Saldini |
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ENRICO ARBARELLO, Università di Roma La Sapienza VARIETA' DI PRYM RELATIVE ASSOCIATE A UNA SUPERFICIE DI ENRIQUES. Lunedì 28 Gennaio 2013, ore 17:00 Università di Milano, Dipartimento di Matematica, Via Saldini | |
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IGOR HERBUT, Simon Fraser University QUANTUM NUMBERS OF TOPOLOGICAL DEFECTS AND REAL CLIFFORD ALGEBRAS IN DIRAC SYSTEMS Lunedì 21 Gennaio 2013, ore 17:00 Università di Milano, Dipartimento di Matematica |
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JAMES ROBINSON, Warwick University INTERPOLATION AND LADYZHENSKAYA INEQUALITY IN A COUPLED ELLIPITIC-PARABOLIC PROBLEM Martedì 27 Novembre 2012, ore 17:00 Politecnico di Milano, Dipartimento di Matematica |
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Abstract
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In 1985 Moffatt proposed the method of magnetic relaxation to construct stationary Euler flows with non-trivial topology. The idea is to take an initial magnetic field and let it evolve under the dynamics of the MHD system with zero viscosity; the time asymptotic limit of the magnetic field should then yield a function that satisfies the stationary Euler equations.
Since the MHD equations are only used to produce the limiting field, the problem can be changed in a number of ways and still (at least heuristically) provide a stationary Euler flow.
In this talk I will discuss a simplification of the system in which the fluid evolution is replaced by an elliptic equation. Our aim is to show that the resulting system is locally well-posed. Despite the apparent simplicity of the equations it turns out that this requires results that are at the limit of what is available - elliptic regularity in $L^1$, the limiting case of the Aubin-Lions compactness theorem, and a strengthened form of the Ladyzehnskaya inequality derived using the theory of interpolation. |
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