Markov processes and magneto-hydrodynamic systems

We derive a stochastic interpretation of a generalised solution of the Cauchy problem for a 3-dimensional magneto-hydrodynamic system, called MHD-Burgerssystem. We construct a mollified MHD-Burgers system and prove the the existence and uniqueness of a measure-valued solution of the Cauchy problem for this system. Finally, we justify a limiting procedure with respect to a mollification parameter and thus prove existence and uniqueness of the Cauchy problem solution for the original MHD-Burgers system. We construct as well a probabilistic representation of this solution.