Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation
DOI10.3934/CPAA.2020247zbMath1460.35334arXiv1911.04041OpenAlexW3092821308MaRDI QIDQ2658688
Publication date: 23 March 2021
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.04041
low regularity solutionsnormal form reductionfourth order nonlinear Schrödinger equation\( U^p\) and \(V^p\) spacesfrequency dependent time scale
Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Weak solutions to PDEs (35D30) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dispersive equations and nonlinear waves. Generalized Korteweg-de Vries, nonlinear Schrödinger, wave and Schrödinger maps
- Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
- Global well-posedness of the KP-I initial-value problem in the energy space
- Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
- The cubic fourth-order Schrödinger equation
- Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
- Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
- Periodic fourth-order cubic NLS: local well-posedness and non-squeezing property
- Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
- Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
- On the ill-posedness of some canonical dispersive equations.
- The global Cauchy problem and scattering of solutions for nonlinear Schrödinger equations in \(H^s\).
- Energy and local energy bounds for the 1-d cubic NLS equation in \(H^{-\frac{1}{4}}\)
- Lyapunov approach to the soliton stability in highly dispersive systems. I: Fourth order nonlinear Schrödinger equations
- A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
- A priori bounds for KdV equation below \(H^{- \frac{3}{4}}\)
- Global Well-Posedness for Schrödinger Equations with Derivative
- Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
- GLOBAL WELL-POSEDNESS OF THE PERIODIC CUBIC FOURTH ORDER NLS IN NEGATIVE SOBOLEV SPACES
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- Low regularity a priori bounds for the modified Korteweg-de Vries equation
- Dispersion estimates for fourth order Schrödinger equations
- A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
This page was built for publication: Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation