| 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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