Finite-time blowup for a complex Ginzburg-Landau equation with linear driving

Thierry Cazenave, João Paulo Dias, Mário Figueira

In this paper, we consider the complex Ginzburg--Landau equation $u_t=e^{i\theta }[\Delta u+|u{|}^{\alpha }u]+\gamma u$ on ${\mathbb{R}}^N$, where $\alpha >0$, $\gamma \in \mathbb{R}$ and $-\pi /2<\theta <\pi /2$. By convexity argume…