Finite time blow-up for the nonlinear Schrödinger equation in trapped dipolar quantum gases with arbitrarily positive initial energy
Abstract In this paper, we study the blow-up criterion for the following nonlinear Schrödinger equation arising in trapped dipolar quantum gases: i ∂ t u = − 1 2 Δ u + a 2 ( x 1 2 + x 2 2 + x 3 2 ) u + λ 1 | u | 2 u + λ 2 ( K ∗ | u | 2 ) u , ( t , x ) ∈ [ 0 , T ∗ ) × R 3 . $$i\partial _{t}u=-\frac{1...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01358-9 |