Non-homogeneous initial boundary value problems for the biharmonic Schrodinger equation on an interval

In this paper we consider the initial boundary value problem (IBVP) for the nonlinear biharmonic Schrodinger equation posed on a bounded interval $(0,L)$ with non-homogeneous Navier or Dirichlet boundary conditions, respectively. For Navier boundary IBVP, we set up its local well-posedness if the initial data lies in $H^s(0, L)$ with $sgeq 0$ and $s eq n+1/2, nin mathbb{N}$, and the boundary data are selected from the appropriate spaces with optimal regularities, i.e., the $j$-th order data are chosen in $H_{loc}^{(s+3-j)/4}(mathbb {R}^+)$, for $j=0,2$. For Dirichlet boundary IBVP the corresponding local well-posedness is obtained when $s>10/7$ and $s eq n+1/2, nin mathbb{N}$, and the boundary data are selected from the appropriate spaces with optimal regularities, i.e., the $j$-th order data are chosen in $H_{loc}^{(s+3-j)/4}(mathbb {R}^+)$, for $j=0,1$.