%0 Journal Article
%T Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
%A Thierry Cazenave
%A Jo£żo Paulo Dias
%A M¨˘rio Figueira
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00028-014-0220-z
%X 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 $\alpha >0$, $\gamma \in \R$ 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.
%U http://arxiv.org/abs/1310.0191v1