AAM  >> Vol. 5 No. 4 (November 2016)

    Blow-Up Criteria for a Kind of Fourth Order Nonlinear Schro¨dinger Equations

  • 全文下载: PDF(560KB) HTML   XML   PP.672-682   DOI: 10.12677/AAM.2016.54079  
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米彩莲,卢美虹,杨晗:西南交通大学数学学院,四川 成都

非线性Schro¨dinger方程初值问题B-G型不等式整体解爆破准则Nonlinear Schro¨dinger Equation Initial Value Problem B-G Type Inequality Global Solution Blow-Up Criteria



The initial-boundary value problem for a kind of fourth order nonlinear Schro¨dinger equations is studied in this paper. Firstly, with the help of the semi-group theory, the existence and uniqueness of local solution of initial value problem is obtained. Secondly, a new global existence criterion for the classical solution is given by using B-G inequality, namely, that whether the solution globally exists is determined by whether its H2 norm blows up.

米彩莲, 卢美虹, 杨晗. 一类四阶非线性Schro¨dinger方程的爆破准则[J]. 应用数学进展, 2016, 5(4): 672-682. http://dx.doi.org/10.12677/AAM.2016.54079


[1] Brézis, H. and Gallouët, T. (1980) Nonlinear Schrödinger Evolution Equations. Nonlinear Analysis: Theory, Methods and Applications, 4, 677-681.
[2] Tsutsumi, M. (1989) On Smooth Solutions to the Initial-Boundary Value Problem for the Nonlinear Schrödinger Equation in Two Space Dimensions. Nonlinear Analysis: Theory, Methods and Applications, 13, 1051-1056.
[3] Ozawa, T. and Visciglia, N. (2015) An Improvement on the Brézis-Gallouët Technique for 2D NLS and 1D Half-Wave Equation. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 33, 1069-1079.
[4] Karpman, V.I. and Shagalov, A.G. (2000) Stability of Solitons Described by Nonlinear Schrödinger-Type Equations with Higher-Order Dispersion. Physica D: Nonlinear Phenomena, 144, 194-210.
[5] Zhu, S., Yang, H. and Zhang, J. (2011) Blow-Up of Rough Solutions to the Fourth-Order Nonlinear Schrödinger Equation. Nonlinear Analysis: Theory, Methods and Applications, 74, 6186-6201.
[6] Zheng, S.M. (2004) Nonlinear Evolution Equations. Chapman & Hall/CRC, London, 56-57.