Noticias en español
ALMOST DESCRIPTION OF DECAY FOR HAMILTONIAN ABCD SYSTEM CHULKWANG KWAK
ABSTRACT The Boussinesq abcd system was originally derived by Bona, Chen and Saut [J. Nonlinear. Sci. (2002)] as first order 2-wave approximations of the incompressible and irrotational, two dimensional water wave equations in the shallow water wave regime. Among many particular regimes, the Hamiltonian generic regime is characterized by the setting b = d > 0 and a,c < 0. It is known that the system in this regime is globally well-posed for small data in the energy space H1 × H1 by Bona, Chen and Saut [Nonlinearity (2004)]. In this talk, we are going to discuss about the decay of small...
Read MoreA critical Poincaré-Sobolev inequality.
Abstract: We study a specific Poincaré-Sobolev inequality in bounded domains, that has recently been used to prove a semi-classical bound on the kinetic energy of fermionic many-body states. The corresponding inequality in the entire space is precisely scale invariant and this gives rise to an interesting phenomenon. Optimizers exist for some (most ?) domains and do not exist for some other domains, at least for the isosceles triangle in two dimensions. In this talk, I will discuss bounds on the constant in the inequality and the proofs of existence and non-existence. This is...
Read More“On the non-local Lazer-McKenna conjecture with superlinear potential under a partial symmetry condition on the domain: Critical and supercritical cases”
Abstract: “In 1983 A. Lazer and P.J. McKenna conjectured that the Ambrosetti-Prodi type problems have an unbounded number of solutions as a defined parameter grows to infinity. There were not results on this conjecture, other than the one dimensional case, until 2003 by Breuer . In this talk we will see the existence of a family of solutions indexed by a real number for the non-local problem with superlinear potential under a partial symmetry condition on the domain”
Read MoreOn domain decomposition preconditioners for finite element approximations of the Helmholtz equation using absorption.
Abstracta: (adjunto)
Read MoreTwo-layer shallow-water internal waves: stability and shocks in mixed type PDEs
Abstract: We study the problem of long waves at the interface of two fluid layers of different densities and present three main results: (i) In the weak stratification (Boussinesq) case, the equations of mixed-type are well posed for times up to breaking if the initial data is in the hyperbolic region of phase space. The physical interpretation of this result is that a type of nonlinear stability holds for sufficiently large Richardson number (ii) In the general case there may be initially hyperbolic data that exit into the elliptic region (i.e. the fluid undergoes spontaneous shear...
Read MoreThe Landau-Lifshitz-Gilbert equation with rough initial data
Abstract: In this talk we will consider the Landau-Lifshitz-Gilbert equation, a model describing the dynamics for the spin in ferromagnetic materials. We will discuss the Cauchy problem with initial conditions that are not in the standard Sobolev spaces, but are in the BMO (bounded mean oscillation) space. By using the stereographic projection, this problem is related to the Cauchy problem for a nonlinear Schrodinger equation with rough initial data.
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