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We highlight a fundamental ill-posedness issue for nonlinear stochastic waveequations driven by a fractional noise. Namely, if the noise becomes too rough(i.e., the sum of its Hurst indexes becomes too small), then there isessentially no hope to provide an interpretation of the model, whether directlyor through a Wick-type renormalization procedure. This phenomenon can becompared with the situation of a general SDE driven by a two-dimensionalfractional noise of index $H\leq \frac{1}{4}$. Our results clarify and extendprevious similar properties exhibited in [3] or in [14].

On ill-posedness of nonlinear stochastic wave equations driven by rough noise