Difficulties in obtaining finite time blowup for fourth-order semilinear Schrödinger equations in the variational method frame
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Date
2019-06-24
Authors
Xu, Runzhang
Lin, Qiang
Chen, Shaohua
Wen, Guojun
Lian, Wei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the Cauchy problem for fourth-order semilinear Schrodinger equations. By constructing a variational problem and some invariant manifolds, we prove the existence of a global solution. Then we analyze the difficulties in proving the finite time blowup of the solution for the corresponding problem in the frame of the variational method. Understanding the finite time blowup of solutions, without radial initial data, still remains an open problem.
Description
Keywords
Fourth-order Schrödinger equation, Global solution, Blowup, Variational problem, Invariant manifolds
Citation
Xu, R., Lin, Q., Chen, S., Wen, G., & Lian, W. (2019). Difficulties in obtaining finite time blowup for fourth-order semilinear Schrödinger equations in the variational method frame. <i>Electronic Journal of Differential Equations, 2019</i>(83), pp. 1-22.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.