## The Brezis-Nirenberg Problem on S^n, in spaces of fractional dimension.

Abstract: We consider the nonlinear eigenvalue problem, -\Delta_{\mathbb{S^n}} u = \lambda u + |u|^{4/(n-2)} u, with $u \in H_0^1(\Omega)$, where $\Omega$ is a geodesic ball in S^n. In dimension 3, this problem was considered by Bandle and Benguria. For positive radial solutions of this problem one is led to an ordinary differential equation (ODE) that still makes sense when n is a real rather than a natural number. Here we consider precisely that situation with 2<n<4. Our main result is that in this case one has a positive solution if and only if $\lambda \ge...

Read More## Asymptotic Stability of solitons of the high dimensional Zakharov-Kuznetsov equation

Abstract: In this talk I will discuss a recent work with R. Cote, D. Pilod and G. Simpson, where we consider solitons of the high dimensional Zakharov-Kuznetsov equation, a model of plasma ions in Physics. In particular, we prove that solitons are strongly asymptotically stable in the energy space, in a particular region of the plane determined by natural geometrical and dispersive constraints. To prove this result we extend to the high dimensional case several tools coming from the one-dimensional setting (generalized KdV equations), introduced by Martel and Merle. However, some new...

Read More## Vortex-type solutions to a magnetic Choquard equation.

http://www.dim.uchile.cl/~cmunoz/Dora.pdf

Read More## Survey on blow up for the critical generalized Korteweg-de Vries equation

Abstract: We will review recent results with Frank Merle and Pierre Raphael (and also partly with Kenji Nakanishi) on blow up for critical generalized Korteweg-de Vries equation, and more generally on the classification of solutions close to the solitons.

Read More## Dynamics of topological defects in nonlinear Hamiltonian PDEs

Blanco Encalada 2010 Sala B101

Read More## Dynamics of topological defects in nonlinear Hamiltonian PDEs

Blanco Encalada 2010 Sala B101

Read More