Mathematical Research Letters

Volume 9 (2002)

Number 3

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

Pages: 323 – 335



N. Burq

P. Gérard

N. Tzvetkov


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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