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- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Springer International Publishing
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-015-0298-y
- Publisher site
- See Article on Publisher Site
Abstract
We consider the supercritical inhomogeneous nonlinear Schrödinger equation $$i\partial_t u+\Delta u+|x|^{-b}|u|^{2\sigma}u=0,$$ i ∂ t u + Δ u + | x | - b | u | 2 σ u = 0 , where $${(2 - b)/N < \sigma < (2 - b)/(N-2)}$$ ( 2 - b ) / N < σ < ( 2 - b ) / ( N - 2 ) and $${0 < b < \rm min\{2,N\}}$$ 0 < b < min { 2 , N } . We prove a Gagliardo–Nirenberg-type estimate and use it to establish sufficient conditions for global existence and blow-up in $${H^1(\mathbb{R}^N)}$$ H 1 ( R N ) .
Journal
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2016