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 . 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
| Yongsheng Li |
School of Mathematics
South China University of Technology
Guangzhou, Guangdong 510640, China
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