Stochastic fluid dynamics equations with multiplicative noise

In the first two chapters, a concise introduction to stochastic integration in Hilbert spaces is given. In the third chapter, a stochastic Leray-alpha model of Euler equations, obtained by adding a Stratonovich multiplicative noise to the deterministic system, is studied. The main result is the existence and uniqueness in law of weak solutions (both in variational and probabilistic sense) satisfying an energy inequality; continuous dependence on the data of the problem is also shown. In the last chapter, further properties of the model, such as regularity of solutions and anomalous dissipation of energy, are studied.