Yuanyuan Ren, Yongsheng Li
Abstract:
In this article we study the Cauchy problem of the nonlinear Schrodinger equations
without gauge invariance
where 1<p1, p2<1+4/n and
.
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.
Show me the PDF file (357 KB), TEX file for this article.
 |
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 |
Return to the EJDE web page