Electron. J. Differential Equations, Vol. 2021 (2021), No. 24, pp. 1-13.

Small data blow-up of solutions to nonlinear Schrodinger equations without gauge invariance in L^2

Yuanyuan Ren, Yongsheng Li

In this article we study the Cauchy problem of the nonlinear Schrodinger equations without gauge invariance

where 1<p1, p2<1+4/n and $\lambda\in \mathbb{C}\backslash\{0\}$. We first prove the existence of a local solution with initial data in L2(Rn). Then under a suitable condition on the initial data, we show that the L2-norm of the solution must blow up in finite time although the initial data are arbitrarily small. As a by-product, we also obtain an upper bound of the maximal existence time of the solution.

Submitted February 15, 2018. Published March 31, 2021.
Math Subject Classifications: 35Q55, 35B44.
Key Words: Nonlinear Schrodinger equations; weak solution; blow up of solutions.

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Yuanyuan Ren
School of Computer Science and Technology
Dongguan University of Technology
Dongguan, Guangdong 523808, China
email: renyuanzhpp@163.com
  Yongsheng Li
School of Mathematics
South China University of Technology
Guangzhou, Guangdong 510640, China
email: yshli@scut.edu.cn

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