Nonlinear Schrödinger equation, differentiation by parts and modulation spaces View Full Text


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Article Info

DATE

2019-04-02

AUTHORS

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann, Nikolaos Pattakos

ABSTRACT

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in the modulation space Mp,qs(R) where 1≤q≤2, 2≤p<10q′q′+6 and s≥0. Moreover, for either 1≤q≤32,s≥0 and 2≤p≤3 or 3223-1q and 2≤p≤3 or 181123-1q and 2≤p<10q′q′+6 we show that the Cauchy problem is unconditionally wellposed in Mp,qs(R). This improves Pattakos (J Fourier Anal Appl, 2018. 10.1007/s00041-018-09655-9), where the case p=2 was considered and the differentiation-by-parts technique was introduced to a problem with continuous Fourier variable. Here, the same technique is used, but more delicate estimates are necessary for p≠2. More... »

PAGES

1-41

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-019-00501-z

DOI

http://dx.doi.org/10.1007/s00028-019-00501-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1113199552


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