Global well-posedness of the two-dimensional Benjamin equation in the energy space

In this paper, the global well-posedness of the Cauchy problem for the two-dimensional Benjamin equation ∂tu+∂x3u−ϵH∂x2u−∂x−1∂y2u+∂x(u2∕2)=0,u(x,y,0)=ϕ(x,y)in the energy space E1={u:‖u‖L2+‖∂xu‖L2+‖∂x−1∂yu‖L2<∞} is obtained.