Long time dynamics of the 3D radial NLS with the combined terms
| Autor: | Jianwei Yang, Gui Xiang Xu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Scattering
Applied Mathematics General Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Perturbation (astronomy) Threshold energy 01 natural sciences symbols.namesake Time dynamics 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Algebraic number Ground state Nonlinear Sciences::Pattern Formation and Solitons Nonlinear Schrödinger equation Mathematical physics Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 32:521-540 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-016-5401-y |
| Popis: | In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation (NLS) with the combined terms $$i{u_t} + \Delta u = - {\left| u \right|^4}u + {\left| u \right|^{p - 1}}u,\;1 + \frac{4}{3} < p < 5$$ in energy space H1(ℝ3). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767–808 (2013)] to all mass supercritical, energy subcritical perturbation. |
| Databáze: | OpenAIRE |
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