Electron. J. Diff. Equ., Vol. 2015 (2015), No. 312, pp. 1-10.

Nonexistence of non-trivial global weak solutions for higher-order nonlinear Schrodinger equations

Abderrazak Nabti

Abstract:
We study the initial-value problem for the higher-order nonlinear Schrodinger equation
$$ i\partial_{t}u-(-\Delta)^{m}u=\lambda| u|^{p}, $$
subject to the initial data
$$ u(x,0)=f(x), $$
where $u=u(x,t)\in\mathbb{C}$ is a complex-valued function, $(x,t)\in\mathbb{R}^{N}\times[0,+\infty)$, $p>1$, $m\geq 1$, $\lambda\in\mathbb{C}\backslash\{0\},$ and $f(x)$ is a given complex-valued function. We prove nonexistence of a nontrivial global weak solution. Furthermore, we prove that the $L^2$-norm of the local in time $L^2$-solution blows up at a finite time.

Submitted October 20, 2015. Published December 21, 2015.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger equation; global solution; blowup.

Show me the PDF file (248 KB), TEX file, and other files for this article.

Abderrazak Nabti
Laboratoire de Mathématiques, Image et Applications
EA 3165, Université de La Rochelle
P&ocric;le sciences et Technologies
Avenue Michel Crépeau, 17000
La Rochelle, France
email: nabtia1@gmail.com

Return to the EJDE web page