Noticias en español
Well-Posedness results for non-isotropic perturbations of the nonlinear Schrödinger equation on cylindrical domains
Abstract: We consider a non-isotropically perturbed nonlinear Schrödinger equation posed on two-dimensional cylindrical domains of the form T×R T and R×T. This equation arises in models describing wave propagation in fiber arrays. In this talk, we present several well-posedness results for initial data belonging to Sobolev spaces. For the cylindrical domain T×R, we establish global well-posedness in L^2xL^2 for small initial data by proving an L^4 – L^2 Strichartz-type inequality. In the case of the domain R×T, we were unable to adapt the same estimate, so we employed a different...
Read MoreThe steady Navier-Stokes equations in a system of unbounded channels with sources and sinks
Abstract: The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply–connected and the fluxes are not assumed to be small. In this very general setting, we prove the existence of a solution with a uniformly bounded Dirichlet integral in every compact subset. This is a generalization of the classical Ladyzhenskaya–Solonnikov result obtained under the additional assumption...
Read MoreExploring elliptic problems with Choquard nonlinearity
Abstract: In this talk, we investigate the existence of weak solutions for elliptic problems involving Choquard nonlinearity. These equations have attracted significant attention due to their ability to model long-range interactions in various real-world applications. A key concept in solving PDEs is that of weak solutions. These solutions satisfy the integral form of the PDE and are useful when classical solutions may not exist or are challenging to compute. This makes them exceedingly valuable in practical applications. We will use Variational methods to solve the PDEs. This technique...
Read MoreQuantum dissipative systems.
Abstract: The problem of modeling dissipative effects in quantum physics dates back to the 1970s. After reviewing the main challenges associated with developing such models, I will present a specific model introduced by Bruneau and De Bièvre in the early 2000s. This model describes the interactions between a classical particle and an abstract environment, where the environment acts on the classical particle as a linear friction force. One of the key strengths of this approach is that it can be naturally extended to the quantum setting. In the second part, I will discuss the dynamical...
Read MoreThe role of Korteweg-de Vries symmetries in the partition function of extremal Black Holes.
Abstract: Abstract: In this talk, we will explore the role of generalized symmetries—symmetry groups that classify families of partial differential equations—in identifying fundamental symmetries in physics. We will also examine how this framework is crucial for defining conservation laws, building on Noether’s theorems and the contribution of Sophus Lie to the understanding of continuous symmetries. We focus on gravity, particularly within the Hamiltonian formalism, and highlight the importance of surface integrals to define conserved quantities, as shown in the pioneering work of...
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