| Abstract: |
| We develop a so-called generalized dynamical rescaling method to study singularity
formation in the complex Ginzburg-Landau equation (CGL). This innovative technique enables
us to capture all relevant symmetries of the problem, allowing us to directly demonstrate a full
stability of constructed blowup solutions. One of the advantages of our approach is its ability
to circumvent spectral decomposition, which is often complex for problems involving non-self-
adjoint operators. Additionally, the (CGL) system lacks a variational structure, making standard
energy-type methods difficult to apply. By employing the amplitude-phase representation, we
establish a robust analysis framework that enforces vanishing conditions through a carefully
chosen normalization and utilizes weighted energy estimates. |
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