Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations

Blow-up phenomena ofvweakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equationsvis shown by a straightforward ODE approach not so-called test-function method, which gives the natural blow-up rate. The difficulty of the proof is that, unlike the single case, terms which come from the fact that the Laplacian cannot be absorbed into the weakly coupled nonlinearities. A similar ODE approach is applied to heat systems by Mochizuki to obtain the lower estimate of lifespan.