New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
Abstract
We consider in this article the weakly coupled system of wave equations in the scale-invariant case and with time-derivative nonlinearities. Under the usual assumption of small initial data, we obtain an improvement of the delimitation of the blow-up region by obtaining a new candidate for the critical curve. More precisely, we enhance the results obtained in Palmieri for the system under consideration in the present work. We believe that our result is optimal in the sense that beyond the blow-up region obtained here we may conjecture the global existence of the solution.
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