arXiv Analytics

Sign in

arXiv:1110.6602 [math.AP]AbstractReferencesReviewsResources

The lack of compactness in the Sobolev-Strichartz inequalities

Luca Fanelli, Nicola Visciglia

Published 2011-10-30Version 1

We provide a general method to decompose any bounded sequence in $\dot H^s$ 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-G\'erard and Keraani in the cases of the wave and Schr\"odinger equations, and is adaptable to a large class of propagators, including those which are matrix-valued.

Comments: 13 pages
Categories: math.AP
Subjects: 35J10, 35L05
Related articles: Most relevant | Search more
arXiv:math/0409313 [math.AP] (Published 2004-09-18, updated 2006-01-05)
Agmon-Kato-Kuroda theorems for a large class of perturbations
arXiv:2205.05919 [math.AP] (Published 2022-05-12)
Problems involving the fractional $g$-Laplacian with Lack of Compactness
arXiv:math/0410140 [math.AP] (Published 2004-10-06, updated 2005-01-20)
Compactness of solutions to some geometric fourth-order equations

Links

Toolbox