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arXiv · 1810.10365

Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions

Hyungjin Huh·Dmitry E. Pelinovsky
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Abstract

We address a general system of nonlinear Dirac equations in (1+1) dimensions and prove nonexistence of classical 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 smooth solutions to the nonlinear Dirac equations in (1+1) dimensions do not develop self-similar singularities in a finite time. In the particular case of the cubic Dirac equations, we characterize (unbounded) self-similar solutions in the closed analytical form.

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Hyungjin Huh, Dmitry E. Pelinovsky. 2018-10-24. Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions. https://arxiv.org/abs/1810.10365

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