Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions. (June 2019)

• Record Type: Journal Article
• Authors: Huh, Hyungjin; Pelinovsky, Dmitry E.
• Is Part Of: Applied mathematics letters. Volume 92(2019)
• Page Start: 176
• Page End: 183
• Publication Date: 2019-06
• Subjects: Nonlinear Dirac equations -- Self-similar solutions -- Global existence -- Finite time blowup; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.01.027
• Languages: English
• ISSNs: 0893-9659

Abstract

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.