Mathematical Research Letters

Volume 9 (2002)

Number 3

An instability property of the nonlinear Schrödinger equation on $S^{d}$

Pages: 323 – 335

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n3.a8

Authors

N. Burq

P. Gérard

N. Tzvetkov

Abstract

We consider the NLS on spheres. We describe the nonlinear evolutions of the highest weight spherical harmonics. As a consequence, in contrast with the flat torus, we obtain that the flow map fails to be uniformly continuous for Sobolev regularity above the threshold suggested by a simple scaling argument.

Full Text (PDF format)