Homogeneous initial–boundary value problem of the Rosenau equation posed on a finite interval

This paper considers the IBVP of the Rosenau equation {∂tu+∂t∂x4u+∂xu+u∂xu=0,x∈(0,1),t>0,u(0,x)=u0(x)u(0,t)=∂x2u(0,t)=0,u(1,t)=∂x2u(1,t)=0. It is proved that this IBVP has a unique global distributional solution u∈C([0,T];Hs(0,1))u∈C([0,T];Hs(0,1)) as initial data u0∈Hs(0,1)u0∈Hs(0,1) with s∈[0,4]s∈[0,4]. This is a new global well-posedness result on IBVP of the Rosenau equation with Dirichlet boundary conditions.