Singular quasilinear wave equations

We extend the paradifferential appraoch to quasilinear wave eqauations of Bahouri and Chemin to the case of a quasilinear wave equation with a (random) distributional forcing. I order to do this, we combine their methods with recently developed tools from singular SPDEs, more precisely the Paracontrolled Calculus of Gubinelli, Imkeller and Perkowski. In two dimensions, we obtain a well-posedness result for noises with Hölder-regularity better than -1/8 for generic initial data and for noises with regularity better than -1 with prepared initial data.