Mathematical Research Letters

Volume 9, Issue 3, March 2002 pp. 323-335.

An instability property of the nonlinear Schr\"odinger equation on $S^{d}$

Authors: N. Burq, P. Gérard, and N. Tzvetkov
Author institution: Université Paris Sud

Summary: 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.

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