Global Cauchy problem for the Ostrovsky equation

In this article we consider the initial value problem for the Ostrovsky equation: ∂tu−∂x3u∓∂x−1u+u∂xu=0,x∈R,t∈R,u(x,0)=u0(x),u(x,0)=u0(x), with initial data in Sobolev spaces Hs(R)Hs(R). Using Bourgain spaces, we prove that the problem is globally well-posed for s>−310 for both signs in the equation.