On the stochastic Benjamin–Ono equation

We discuss the Cauchy problem for the stochastic Benjamin–Ono equation in the function class Hs(R), s>3/2. When there is a zero-order dissipation, we also establish the existence of an invariant measure with support in H2(R). Many authors have discussed the Cauchy problem for the deterministic Benjamin–Ono equation. But our results are new for the stochastic Benjamin–Ono equation. Our goal is to extend known results for the deterministic equation to the stochastic equation.