Small data blow-up of solutions to nonlinear Schrodinger equations without gauge invariance in L2
| dc.contributor.author | Ren, Yuanyuan | |
| dc.contributor.author | Li, Yongsheng | |
| dc.date.accessioned | 2021-08-23T14:27:43Z | |
| dc.date.available | 2021-08-23T14:27:43Z | |
| dc.date.issued | 2021-03-31 | |
| dc.description.abstract | In this article we study the Cauchy problem of the nonlinear Schrödinger equations without gauge invariance i∂tu + Δu = λ(|u|p1 + |v|p2, (t, x) ∈ [0, T) x ℝn, i∂tv + Δv = λ(|u|p2 + |v|p1, (t, x) ∈ [0, T) x ℝn, where 1 < p1, p2 < 1 + 4/n and λ ∈ ℂ\{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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Ren, Y., & Li, Y. (2021). Small data blow-up of solutions to nonlinear Schrodinger equations without gauge invariance in L2. <i>Electronic Journal of Differential Equations, 2021</i>(24), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14421 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear Schrödinger equations | |
| dc.subject | Weak solution | |
| dc.subject | Blow up of solutions | |
| dc.title | Small data blow-up of solutions to nonlinear Schrodinger equations without gauge invariance in L2 | |
| dc.type | Article |