We provide a general method to decompose any bounded sequence in Ḣs 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 and Gérard and by 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. © 2012 Elsevier Masson SAS.
The lack of compactness in the Sobolev-Strichartz inequalities / Fanelli, Luca; Nicola, Visciglia. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - ELETTRONICO. - 99:3(2013), pp. 309-320. [10.1016/j.matpur.2012.06.015]
The lack of compactness in the Sobolev-Strichartz inequalities
FANELLI, Luca;
2013
Abstract
We provide a general method to decompose any bounded sequence in Ḣs 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 and Gérard and by 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. © 2012 Elsevier Masson SAS.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
