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

Blow-up phenomena of weakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equations is shown by a straightforward ODE approach, not by the so-called test-function method used in [38] which gives the natural blow-up rate. The difficulty of the proof is that, unlike the single case, terms which come from the Laplacian cannot be absorbed into the weakly coupled nonlinearities. A similar ODE approach is applied to heat systems by Mochizuki [32] to obtain the lower estimate of lifespan