FINITE-TIME BLOWUP FOR A COMPLEX GINZBURG-LANDAU EQUATION

We prove that negative energy solutions of the complex Ginzburg-Landau equation e-(i theta)u(t) = Delta u + vertical bar u vertical bar(alpha)u blow up in finite time, where alpha > 0 and -pi/2 < theta < pi/2. For a fixed initial value u(0), we obtain estimates of the blow-up time T-max(theta) as theta -> +/-pi/2. It turns out that T-max(theta) stays bounded (respectively, goes to infinity) as theta -> +/-pi/2 in the case where the solution of the limiting nonlinear Schrodinger equation blows up in finite time (respectively, is global).