WELL-POSEDNESS OF STOCHASTIC NONLINEAR HEAT AND WAVE EQUATIONS DRIVEN BY SUBORDINATE CYLINDRICAL BROWNIAN NOISES ON THE TWO-DIMENSIONAL TORUS (Nonlinear and Random Waves)

Abstract

In [12], the author studied stochastic nonlinear heat equations and stochastic nonlinear wave equations driven by subordinate cylindrical Brownian noises on the two-dimensional torus by way of renormalization. More precisely, the author studied the local well-posedness of the renormalized version of the equations. In this note, we make some remarks on the global well-posedness of the stochastic nonlinear wave equation with a cubic nonlinearity after we briefly revisit the results in [12].