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

2020/03/20 by Li, Junfeng, Zheng, Chuang
#35Q40 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2003.09337

Abstract

In this paper we consider the initial boundary value problem (IBVP) for the nonlinear biharmonic Schrödinger 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 s≥ 0 and s≠ n+1/2, n∈ 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≠ n+1/2, n∈ 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.

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