English

$H^s$ Bounds for the Derivative Nonlinear Schr\"odinger Equation

Analysis of PDEs 2022-07-20 v1
Authors: Hajer Bahouri , Trevor M. Leslie , Galina Perelman
View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We study the derivative nonlinear Schr\"odinger equation on the real line and obtain global-in-time bounds on high order Sobolev norms.

Keywords

derivative nonlinear schrödinger equation sobolev norms global bounds real line

Cite

@article{arxiv.2107.12297,
  title  = {$H^s$ Bounds for the Derivative Nonlinear Schr\"odinger Equation},
  author = {Hajer Bahouri and Trevor M. Leslie and Galina Perelman},
  journal= {arXiv preprint arXiv:2107.12297},
  year   = {2022}
}

Comments

20 pages

Related papers

View all related →
Analysis of PDEs · Mathematics
Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schr\"odinger Equation
Bradley Isom, Dionyssios Mantzavinos, Atanas Stefanov
2020-12-21
Analysis of PDEs · Mathematics
Global well-posedness of the derivative nonlinear Schr\"odinger equation with periodic boundary condition in $H^{\frac12}$
Razvan Mosincat
2016-08-25
Analysis of PDEs · Mathematics
Global Existence for the Derivative Nonlinear Schr\"{o}dinger Equation with Arbitrary Spectral Singularities
Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem
2020-07-29
Analysis of PDEs · Mathematics
Higher order nonlinear Schr\"odinger equation in domains with moving boundaries
Raul Nina Mollisaca, Mauricio Sepúlveda Cortés, Rodfigo Véjar Asém, Octavio Vera Villagrán
2025-05-07
Analysis of PDEs · Mathematics
A priori bounds and weak solutions for the nonlinear Schr\"odinger equation in Sobolev spaces of negative order
Michael Christ, James Colliander, Terence Tao
2007-05-23
Exactly Solvable and Integrable Systems · Physics
Long-time asymptotics for the derivative nonlinear Schr\"odinger equation on the half-line
L. K. Arruda, J. Lenells
2017-08-24
Analysis of PDEs · Mathematics
Lifespan of strong solutions to the periodic derivative nonlinear Schr\"odinger equation
Kazumasa Fujiwara, Tohru Ozawa
2018-06-06
Analysis of PDEs · Mathematics
Quadratic lifespan and growth of Sobolev norms for derivative Schr\"odinger equations on generic tori
Roberto Feola, Riccardo Montalto
2021-03-19
Analysis of PDEs · Mathematics
WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity
Rémi Carles, Clément Gallo
2020-12-16
Analysis of PDEs · Mathematics
On boundary controllability for the higher order nonlinear Schr\"odinger equation
Andrei V. Faminskii
2023-12-07
Analysis of PDEs · Mathematics
Global well-posedness for the derivative nonlinear Schr\"odinger equation
Hajer Bahouri, Galina Perelman
2020-12-04
Analysis of PDEs · Mathematics
Unconditional uniqueness for the derivative nonlinear Schr\"odinger equation on the real line
Razvan Mosincat, Haewon Yoon
2018-10-24
Analysis of PDEs · Mathematics
Well-posedness for a generalized derivative nonlinear Schr\"odinger equation
Masayuki Hayashi, Tohru Ozawa
2025-02-27
Dynamical Systems · Mathematics
Almost global solutions to two classes of 1-d Hamiltonian Derivative Nonlinear Schr\"odinger equations
Jing Zhang
2019-02-19
Analysis of PDEs · Mathematics
Hyperbolic nonlinear Schr\"odinger equations on $\mathbb{R}\times \mathbb{T}$
Engin Başakoğlu, Chenmin Sun, Nikolay Tzvetkov, Yuzhao Wang
2026-03-11
Analysis of PDEs · Mathematics
On The Cauchy Problem For A Derivative Nonlinear Schr{\"o}Dinger Equation With Nonvanishing Boundary Conditions
Phan van Tin
2021-01-25
Analysis of PDEs · Mathematics
Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrodinger Equations on $S^1$
Vedran Sohinger
2024-07-08
Analysis of PDEs · Mathematics
On some nonlinear Schr\"odinger equations in $\bbr^N$
Juncheng Wei, Yuanze Wu
2021-12-10
Analysis of PDEs · Mathematics
On the growth of high Sobolev norms of the cubic nonlinear Schr\"odinger equation on $\mathbb{R}\times \mathbb{T}$
Mingming Deng, Kailong Yang
2023-02-02
Exactly Solvable and Integrable Systems · Physics
The solution of the global relation for the derivative nonlinear Schr\"odinger equation on the half-line
Jonatan Lenells
2010-11-15
Exactly Solvable and Integrable Systems · Physics
An integrable generalization of the nonlinear Schr\"odinger equation on the half-line and solitons
J. Lenells, A. S. Fokas
2009-09-30
Mathematical Physics · Physics
Linear nonlocal problem for the abstract time-dependent non-homogeneous Schr\"odinger equation
Dmytro Sytnyk, Roderick Melnik
2018-08-31
Analysis of PDEs · Mathematics
Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
Jiaqi Liu, Peter Perry, Catherine Sulem
2016-08-16
Analysis of PDEs · Mathematics
Higher order asymptotics for the nonlinear Schr\"odinger equation
Jiaqi Liu, Changhua Yang
2024-12-17
Analysis of PDEs · Mathematics
Nonlinear Schr\"odinger equation with bounded magnetic field
Giuseppe Devillanova, Cyril Tintarev
2019-11-14