Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 53, Number 3 (2013), 629-672.
Blowup and scattering problems for the nonlinear Schrödinger equations
We consider -supercritical and -subcritical focusing nonlinear Schrödinger equations. We introduce a subset of for , and investigate behavior of the solutions with initial data in this set. To this end, we divide into two disjoint components and . Then, it turns out that any solution starting from a datum in behaves asymptotically free, and solution starting from a datum in blows up or grows up, from which we find that the ground state has two unstable directions. Our result is an extension of the one by Duyckaerts, Holmer, and Roudenko to the general powers and dimensions, and our argument mostly follows the idea of Kenig and Merle.
Kyoto J. Math., Volume 53, Number 3 (2013), 629-672.
First available in Project Euclid: 19 August 2013
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Akahori, Takafumi; Nawa, Hayato. Blowup and scattering problems for the nonlinear Schrödinger equations. Kyoto J. Math. 53 (2013), no. 3, 629--672. doi:10.1215/21562261-2265914. https://projecteuclid.org/euclid.kjm/1376917628