45 citations · 85 across the 21 of their papers we have counts for
5 papers · 2 filters
Carleman estimates and necessary conditions for the existence of waveguides
Luis Escauriaza, Luca Fanelli, Luis Vega
We study via Carleman estimates the sharpest possible exponential decay for {\it waveguide} solutions to the Laplace equation $$(\partial^2_t+\triangle)u=Vu+W\cdot(\partial_t,\nabl…
On the stability of self-similar solutions of 1D cubic Schrodinger equations
Susana Gutierrez, Luis Vega
In this paper we will study the stability properties of self-similar solutions of 1-d cubic NLS equations with time-dependent coefficients of the form iu_t+u_{xx}+\frac{u}{2} (|u|^…
Selfsimilar solutions of the binormal flow and their stability
Valeria Banica, Luis Vega
We review some recent results concerning the evolution of a vortex filament and its relation to the cubic non-linear Schrödinger equation. Selfsimilar solutions and questions relat…
Existence of maximizers for Sobolev-Strichartz inequalities
Luca Fanelli, Luis Vega, Nicola Visciglia
We prove the existence of maximizers of Sobolev-Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperb…
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation
Miguel A. Alejo, Claudio Muñoz, Luis Vega
Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingl…