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Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions
- Authors
- Huh, Hyungjin; Pelinovsky, Dmitry E.
- Issue Date
- Jun-2019
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- Keywords
- Nonlinear Dirac equations; Self-similar solutions; Global existence; Finite time blowup
- Citation
- APPLIED MATHEMATICS LETTERS, v.92, pp 176 - 183
- Pages
- 8
- Journal Title
- APPLIED MATHEMATICS LETTERS
- Volume
- 92
- Start Page
- 176
- End Page
- 183
- ISSN
- 0893-9659
- Abstract
- We address a general system of nonlinear Dirac equations in (1+1) dimensions and prove nonexistence of self-similar blowup solutions in the space of bounded functions. While this argument does not exclude the possibility of finite-time blowup, it still suggests that self-similar singularities do not develop in the nonlinear Dirac equations in (1+1) dimensions in a finite time. In the particular case of the cubic Dirac equations, we characterize (unbounded) self-similar solutions in the closed analytical form. (C) 2019 Elsevier Ltd. All rights reserved.
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