Noticias en español
Integrable Geometries in AdS_{3}
Abstract: In this talk we discuss the geometrization of 1+1 integrable systems included in the AKNS integrable system, which contains the Korteweg de-Vries (KDV), modified KDV, sine-Gordon and non-linear Schrödinger equations. This is possible through the construction of a broad class of asymptotic conditions for the gravitational field in three dimensions, reproducing the properties of the AKNS dynamics. We study the consistency, asymptotic symmetry algebra and integrability properties of these novel boundary conditions.
Read MoreSteady-state Navier-Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate.
Abstract: The steady motion of a viscous incompressible fluid in an obstructed finite pipe is modeled through the Navier-Stokes equations with mixed boundary conditions involving the Bernoulli pressure and the tangential velocity on the inlet and outlet of the tube, while a transversal flux rate F is prescribed along the pipe. Existence of a weak solution to such Navier-Stokes system is proved without any restriction on the data by means of the Leray-Schauder Principle, in which the required a priori estimate is obtained by a contradiction argument based on Bernoulli’s law. Through...
Read MoreLipschitz regularity of almost minimizers for a degenerate one-phase Bernoulli-type functional.
Abstract: In this talk, we deal with almost minimizers for the energy functional (,Ω):=∫Ω(|∇()|+{>0}()),>1,(1) where Ω is a bounded domain in ℝ and ≥0. The functional is a generalization to each >1 of the classical one-phase (Bernoulli) energy functional, corresponding to =2 in (1). Almost minimizers of 2 were investigated recently in [2, 1]. However, in [4] D. De Silva and O. Savin provided a different approach with respect to [2, 1], based on nonvariational techniques, to deal with almost minimizers of 2 and their free boundaries. Precisely, inspired by [5], they showed...
Read MoreHamilton–Jacobi problems on graphs and networks.
Abstract: The talk presents some Hamilton–Jacobi problems on networks. The pecu- liarity is that the Hamiltonians on different arcs are unrelated, without any compatibility condition at the vertices. Nevertheless, uniqueness result and comparison principles can be obtained, suitably exploiting the geometry of the network, Our approach consists in associating to the problem on the network a discrete or semidis- crete equation posed on an underlying abstract graph. This allows testing separately the equations on any arc and proving comparison results without using the doubling variable...
Read MoreMinimally implicit Runge-Kutta methods: relativistic resistive magnetohydrodynamic equations and neutrino M1 transport equations.
Abstract: In this talk I will present the minimally implicit Runge-Kutta methods. I will show their application in two different hyperbolic systems of equations with stiff source terms. On one hand, these methods have been sucessfully applied in the evolution of the resistive relativistic magnetohydrodynamic equations following Komissarov (2007) approach. On the other hand, these schemes have been also sucessfully applied in the evolution of the neutrino transport equations within the M1 closure approximation, and used in supernovae simulations. I will conclude the talk with some general...
Read MoreLinear and non-linear stability of collisionless many-particle systems on black hole exteriors.
Abstract: I will present upcoming linear and non-linear stability results concerning the asymptotic behavior of collisionless many-particle systems on black hole exteriors. On the one hand, I will discuss decay properties for solutions to the massive Vlasov equation on Schwarzschild spacetime. On the other hand, I will discuss an asymptotic stability result for the exterior of Schwarzschild as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. I will explain the use of hyperbolic dynamics to obtain decay in time of the energy momentum tensor by considering a...
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