Le but de cette note est de démontrer des estimations de Strichartz optimales avec pertes de dérivées pour l'équation de Schrödinger non elliptique posée sur le tore de dimension 2.Abstract. The purpose of this note is to prove sharp Strichartz estimates with derivative losses for the non elliptic Schrödinger equation posed on the 2 dimensional torus.[5] Y. Wang, Periodic cubic hyperbolic Schrödinger equation on T 2 , preprint.
Abstract. We consider the focusing quintic nonlinear Schrödinger equation posed on a rotationally symmetric surface, typically the sphere S 2 or the two dimensional hyperbolic space H 2 . We prove the existence and the stability of solutions blowing up on a suitable curve with the log log speed. The Euclidean case is handled in [25] and our result shows that the log log rate persists in other geometries with the assumption of a radial symmetry of the manifold.
We consider the hyperbolic-elliptic version of the Davey-Stewartson system with cubic nonlinearity posed on the two dimensional torus. A natural setting for studying blow up solutions for this equation takes place in H s , 1/2 < s < 1. In this paper, we prove a lower bound on the blow up rate for these regularities.
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