Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance
| Autor: | Kuranosuke Nishimura, Nobu Kishimoto, Takahisa Inui |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematics::Analysis of PDEs 01 natural sciences Resonance (particle physics) 010101 applied mathematics Nonlinear system symbols.namesake Quadratic equation FOS: Mathematics symbols 0101 mathematics Finite time Analysis Schrödinger's cat Analysis of PDEs (math.AP) Mathematical physics Mathematics |
| Zdroj: | Nonlinear Analysis. 198:111895 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2020.111895 |
| Popis: | We consider the quadratic nonlinear Schrodinger system i ∂ t u + Δ u = v u ¯ , i ∂ t v + κ Δ v = u 2 , on I × R d , where 1 ≤ d ≤ 6 and κ > 0 . In the lower dimensional case d = 1 , 2 , 3 , it is known that the H 1 -solution is global in time. On the other hand, there are finite time blow-up solutions when d = 4 , 5 , 6 and κ = 1 ∕ 2 . The condition of κ = 1 ∕ 2 is called mass-resonance. In this paper, we prove finite time blow-up under radially symmetric assumption when d = 5 , 6 and κ ≠ 1 ∕ 2 and we show blow-up or grow-up when d = 4 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect