Noticias en español
Persistence and unique continuation principles in weighted spaces for solutions of the fractional Korteweg- de Vries equation.
Abstract: Persistence problems in weighted spaces have been studied for differ- ent dispersive models involving non-local operators. Generally, these equations do not propagate polynomial weights of arbitrary magni- tude, and the maximum decay rate is associated with the dispersive part of the equation. Altogether, this analysis is complemented by unique continuation principles that determine optimal spatial decay. This talk aims to show our results on the preceding questions for a weakly dispersive perturbation of the inviscid Burgers equation, which comprises the Burgers-Hilbert equation...
Read MoreGravitational instantons in AdS: (anti-)self duality, topological terms, and conformal invariance.
Abstract: In this talk, we present some recent developments in obtaining conserved charges and thermodynamics of Euclidean, regular, and stationary solutions in general relativity. The introduction of topological terms renders the Euclidean Einstein-Hilbert on-shell action and Noether-Wald charges finite. The former is proportional to the Chern-Pontryagin index when evaluated at (anti-)self-dual solutions and the resemblance with instantons in Yang-Mills theory is evident. We work out the case of Taub-NUT/Bolt-AdS explicitly and compute the contribution of the Misner string to Wald’s...
Read MoreEnergetic methods for capturing sharp convergence- and metastable-relaxation-rates of gradient flows.
Abstract: (Ver pdf adjunto)
Read MoreScattering via Morawetz estimates for the non-radial inhomogeneous nonlinear Schr ̈odinger equation.
Abstract: The concentration-compactness-rigidity method, pioneered by Kenig and Merle, has become standard in the study of global well-posedness and scattering in the context of dispersive and wave equations. Albeit powerful, it requires building some heavy machinery in order to obtain the desired space-time bounds. In this talk, we present a simpler method, based on Tao’s scattering criterion and on Dodson-Murphy’s Virial/Morawetz inequalities, first proved for the 3d cubic nonlinear Schr ̈odinger (NLS) equation. Tao’s criterion is, in some sense, universal, and it is expected to work in...
Read MoreWave-Structure interactions: oscillating water columns in shallow water.
Abstract: Wave energy converters (WECs) are devices that convert the energy associated with a moving ocean wave into electrical energy. In this talk we present a mathematical model of a particular wave energy converter, the so-called oscillating water columns in shallow water regime. This model can be reformulated as two transmission problems: one is related to the wave motion over the stepped topography and the other one is related to the wave-structure interaction where a fixed partially immersed structure is installed. We analyze the evolution of the contact line between the surface of...
Read MoreSeparation and Interaction energy between domain walls in a nonlocal model.
Abstract: We analyse a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter epsilon > 0. The model gives rise to transition layers, called Néel walls, and we study their behaviour in the limit epsilon -> 0. The analysis has some similarity to the theory of Ginzburg-Landau vortices. In particular, it gives rise to a renormalised energy that determines the interaction (attraction or repulsion) between Néel walls to leading order. But while Ginzburg-Landau vortices show attraction for winding numbers of the same sign and...
Read More