Finite-time blowup for some nonlinear complex Ginzburg-Landau equations

Abstract

In this article, we review finite-time blowup criteria for the family of complex Ginzburg-Landau equations $u_t=e^{i\theta }[\Delta u+|u{|}^{\alpha }u]+\gamma u$ on ${\mathbb{R}}^N$, where $0\le \theta \le \frac{\pi }{2}$, $\alpha >0$ and $\gamma \in \mathbb{R}$. We study in particular the effect of the parameters $\theta$ and $\gamma$, and the dependence of the blowup time on these parameters.

References in corpus (2)

• Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
• Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the $L^2$ critical case