The aim of this course is to study SPDEs in real-valued Hilbert spaces and application of the theory to prove the existence of martingale solutions to a concrete problem (Stochastic non-linear Heat equation or Stochastic constrained Navier-Stokes equation) using the Galerkin approximation, Skorokhod theorem, martingale representation theorem.

Stochastic Analysis in Hilbert Spaces, Wiener Process, Ito Lemma in infinite dimensions, Martingale solutions