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

Abstract

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 arguments we prove that, under certain conditions on $\alpha ,\theta ,\gamma$, a class of solutions with negative initial energy blows up in finite time.

References in corpus (1)

• Finite-time blowup for a complex Ginzburg-Landau equation

Cited by in corpus (2)

• Finite-time blowup for some nonlinear complex Ginzburg-Landau equations
• Local well-posedness of the complex Ginzburg-Landau equation in bounded domains