Global dynamics below the ground state for the focusing Schrödinger equation with a potential
| Autor: | Masaru Hamano, Masahiro Ikeda |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Scattering
010102 general mathematics 01 natural sciences Resonance (particle physics) Schrödinger equation 010101 applied mathematics Nonlinear system symbols.namesake Mathematics (miscellaneous) Quadratic equation symbols 0101 mathematics Ground state Nonlinear Schrödinger equation Schrödinger's cat Mathematics Mathematical physics |
| Zdroj: | Journal of Evolution Equations. 20:1131-1172 |
| ISSN: | 1424-3202 1424-3199 |
| DOI: | 10.1007/s00028-019-00547-z |
| Popis: | In this paper, we consider the nonlinear Schrodinger equation with a real-valued potential $$V=V(x)$$ . We study global behavior of solutions to the equation with data below the ground state under some conditions for the potential V and prove a scattering result and a blowing-up result in mass-supercritical and energy-subcritical. Our proof of the scattering result is based on an argument by Dodson–Murphy (Proc Am Math Soc 145(11):4859–4867, 2017). The proof of the blowing-up or growing-up result without radially symmetric assumption is based on the argument by Du–Wu–Zhang (Discrete Contin Dyn Syst 36(7):3639–3650, 2016). We can exclude the possibility of the growing-up result by the argument (Inui et al. in Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrodinger system without mass resonance, arXiv:1810.09153.; Nakanishi and Schlag in Calc Var Partial Differ Eq 44(1-2):1–45, 2012; Glassey in J Math Phys 18(9):1794–1797, 1977) if “the data and the potential are radially symmetric” or “the data has finite variance.” |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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