On blow-up criterion for the nonlinear Schrödinger equation systems

doi:10.3868/s140-DDD-023-0031-x

Front. Math. China

2023, Vol. 18

Issue (6) : 441-447 https://doi.org/10.3868/s140-DDD-023-0031-x

On blow-up criterion for the nonlinear Schrödinger equation systems

Yili GAO(

)

Center for Applied Mathematics, Tianjin University, Tianjin 300072, China

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Abstract

In this paper, we study the blow-up problem of nonlinear Schrödinger equations

　　　　　　　　 ${i ∂ t v + Δ u + (| u | 2 + | v | 2) u = 0, (t, x) ∈ R 1 + n, i ∂ t v + Δ v + (| u | 2 + | v | 2) v = 0, (t, x) ∈ R 1 + n, u (0, x) = u 0 (x), v (0, x) = v 0 (x),$

and prove that the solution of negative energy $(E (u, v) < 0)$ blows up in finite or infinite time.

Keywords Nonlinear Schrödinger equations blow up negative energy

Online First Date: 27 February 2024 Issue Date: 05 March 2024

Cite this article:

Yili GAO. On blow-up criterion for the nonlinear Schrödinger equation systems[J]. Front. Math. China, 2023, 18(6): 441-447.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0031-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I6/441

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