具有二次相互作用的非线性薛定谔方程组的爆破解
Explosive Solution of Nonlinear Schr?dinger Equations with Quadratic Interactions
摘要: 本文研究了具有一般二次型非线性的薛定谔方程组的爆破结果。我们证明了六维圆柱对称的有限时间爆破解。主要研究方法是基于非质量共振条件下的圆柱对称维里估计。
Abstract: In this paper, we study the blow-up results of Schrödinger’s equations with general quadratic non-linearity. We prove the finite-time blow-up solution of Six-dimensional cylindrical symmetry. The main research method is based on the virial estimation of cylindrical symmetry under the condition of massless resonance.
文章引用：涂佳宝. 具有二次相互作用的非线性薛定谔方程组的爆破解[J]. 理论数学, 2023, 13(5): 1289-1297. https://doi.org/10.12677/PM.2023.135132

参考文献

[1] Noguera, N. and Pastor, A. (2022) Blow-Up Solutions for a System of Schrödinger Equations with General Quadratic Type Nonlinearities in Dimensions Five and Six. Calculus of Variations and Partial Differential Equations, 61, 1-35. [Google Scholar] [CrossRef] 
[2] Dinh, V.D. and Forcella, L. (2021) Blow-Up Results for Sys-tems of Nonlinear Schrödinger Equations with Quadratic Interaction. Zeitschrift für Angewandte Mathematik und Physik, 72, 1-26. [Google Scholar] [CrossRef] 
[3] Hamano, M. (2018) Global Dynamics below the Ground State for the Quadratic Schrödinger System in 5D. arXiv:1805.12245.
[4] Hayashi, N., Li, C. and Naumkin, P.I. (2011) On a System of Nonlinear Schrödinger Equations in 2D. Differential and Integral Equations, 25, 417-434. [Google Scholar] [CrossRef] 
[5] Noguera, N. and Pastor, A. (2021) A System of Schrödinger Equations with General Quadratic-Type Nonlinearities. Communications in Contemporary Mathematics, 23, Article ID: 2050023. [Google Scholar] [CrossRef] 
[6] Hoshino, G. and Ogawa, T. (2013) Analytic Smoothing Effect for a System of Nonlinear Schrödinger Equations. Differential Equations & Applications, 395-408. [Google Scholar] [CrossRef] 
[7] Hoshino, G. and Ogawa, T. (2015) Analytic Smoothing Effect for a System of Schrödinger Equations with Two Wave Interaction. Advances in Difference Equations, 20, 697-716. [Google Scholar] [CrossRef] 
[8] Hoshino, G. and Ozawa, T. (2015) Analytic Smoothing Effect for a System of Schrödinger Equations with Three Wave Interaction. Journal of Mathematical Physics, 56, Article ID: 091513. [Google Scholar] [CrossRef] 
[9] Hoshino, G. (2017) Analytic Smoothing Effect for Global Solutions to a Quadratic System of Nonlinear Schrödinger Equations. Nonlinear Differential Equations and Applications, 24, 1-17. [Google Scholar] [CrossRef] 
[10] Cho, Y. and Ozawa, T. (2009) Sobolev Inequalities with Symmetry. Communications in Contemporary Mathematics, 11, 355-365. [Google Scholar] [CrossRef] 

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