The lack of compactness in the Sobolev-Strichartz inequalities

2011/10/30 by Fanelli, Luca, Visciglia, Nicola
#35J10 #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.6602

Abstract

We provide a general method to decompose any bounded sequence in H^s into linear dispersive profiles generated by an abstract propagator, with a rest which is small in the associated Strichartz norms. The argument is quite different from the one proposed by Bahouri-Gérard and Keraani in the cases of the wave and Schrödinger equations, and is adaptable to a large class of propagators, including those which are matrix-valued.

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