arXiv subjects
Publications and source records attributed to Joe Ghafari.
We prove the existence and uniqueness of a local-in-time solution to the stochastic Cahn-Hilliard equation in space dimensions 1, 2, 3, 4 and 5. Our method relies on the Da Prato-Debussche trick for $d=4$ and paracontrolled distributions for $d=5.$
We prove local well-posedness of the Cahn-Hilliard equation with additive noise. Our method relies on paracontrolled calculus and the Da Prato-Debussche trick.
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.