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The lack of compactness in the Sobolev-Strichartz inequalities

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-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.

preprint2011arXivOpen access
Luca FanelliNicola Visciglia
math.AP
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Luca FanelliNicola Visciglia

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