Year: 2026
Type: preprint
Abstract: We show that singularities of the three-dimensional cubic complex Ginzburg-Landau equation developing from smooth initial data can induce non-uniqueness of solutions after the time of blowup. The solutions we study start as backward self-similar solutions, and the source of the non-uniqueness is an unstable eigenvalue of the linearization around the forward self-similar profile generated by the singularity. We establish the existence of this eigenvalue, and hence the non-uniqueness, by a computer-assisted proof for specific values of the parameters in the equation. The work is in part motivated by similarities to conjectured behavior for the Navier-Stokes equation, with which the complex Ginzburg-Landau equation shares several important properties, such as an energy inequality and the scaling symmetry.
Source: arXiv (Cornell University)
Authors: Dahne, Joel, Šverák, Vladimír
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7212086481