Finite-time blowup for a complex Ginzburg-Landau equation

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-i\theta }{u}_t=\Delta u+|u{|}^{\alpha }u$ blow up in finite time, where α>0 and π/2<θ<π/2. For a fixed initial val…