Regularity properties of the cubic biharmonic Schrödinger equation on the half line

DOI10.1007/S42985-021-00106-7zbMath1483.35197OpenAlexW3195828299WikidataQ114216498 ScholiaQ114216498MaRDI QIDQ825604

Engin Başakoğlu

Publication date: 17 December 2021

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42985-021-00106-7

zbMATH Keywords

smoothinginitial boundary value problemlocal wellposednessglobal wellposedness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for nonlinear higher-order PDEs (35G30) NLS equations (nonlinear Schrödinger equations) (35Q55) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (1)

Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity
• Regularity properties of the cubic nonlinear Schrödinger equation on the half line
• Smoothing and global attractors for the Zakharov system on the torus
• Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces
• Factorization technique for the fourth-order nonlinear Schrödinger equation
• The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line.
• The cubic fourth-order Schrödinger equation
• A smoothing property for the \(L^2\)-critical NLS equations and an application to blowup theory
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation
• Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations
• Well-posedness and ill-posedness for the fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces
• The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line
• Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
• Global existence and asymptotic behavior of solutions to the fourth-order nonlinear Schrödinger equation in the critical case
• Global existence of small solutions for the fourth-order nonlinear Schrödinger equation
• Well-posedness and nonlinear smoothing for the ``good Boussinesq equation on the half-line
• The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament
• Wellposedness for the fourth order nonlinear Schrödinger equations
• Talbot effect for the cubic non-linear Schröedinger equation on the torus
• Dispersive Partial Differential Equations
• Global Smoothing for the Periodic KdV Evolution
• Existence and Uniqueness theory for the fractional Schr\"odinger equation on the torus
• On the inhomogeneous fourth-order nonlinear Schrödinger equation
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Regularity properties of the Zakharov system on the half line
• Fractal solutions of linear and nonlinear dispersive partial differential equations

This page was built for publication: Regularity properties of the cubic biharmonic Schrödinger equation on the half line