Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
arXiv:1812.11079 · doi:10.2140/pjm.2020.309.35
Abstract
This paper deals with the initial-boundary value problem of the biharmonic cubic nonlinear Schrödinger equation in a quarter plane with inhomogeneous Dirichlet-Neumann boundary data. We prove local well-posedness in the low regularity Sobolev spaces introducing Duhamel boundary forcing operator associated to the linear equation to construct solutions on the whole line. With this in hands, the energy and nonlinear estimates allow us to apply Fourier restriction method, introduced by J. Bourgain, to get the main result of the article. Additionally, adaptations of this approach for the biharmonic cubic nonlinear Schrödinger equation on star graphs are also discussed.
arXiv comment26 pages, 2 figures
References in corpus (6)
- The Korteweg-de Vries equation on a metric star graph
- Airy-type evolution equations on star graphs
- Feedback stabilization and boundary controllability of the Korteweg-de Vries equation on a star-shaped network
- Stabilization and control for the biharmonic Schrödinger equation
- The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line
- Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation