Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle

DOI10.1016/j.jde.2021.06.018zbMath1473.35486arXiv2001.06896OpenAlexW3176585547MaRDI QIDQ2042669

Seungly Oh, Atanas G. Stefanov, Dionyssios Mantzavinos, Bradley Isom

Publication date: 21 July 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06896

zbMATH Keywords

nonlinear smoothingperiodic Benjamin-Ono equationpolynomial-in-time bound

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items

Unconditional uniqueness for the Benjamin-Ono equation ⋮ A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A remark on normal forms and the ``upside-down \(I\)-method for periodic NLS: growth of higher Sobolev norms
• Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries equation in low regularity settings
• Smoothing and global attractors for the Zakharov system on the torus
• Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations on \(S^1\).
• Quadratic forms for a 2-D semilinear Schrödinger equation
• On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
• On the global well-posedness of the Benjamin-Ono equation
• Global well-posedness in the energy space for the Benjamin-Ono equation on the circle
• Nonlocal models for nonlinear, dispersive waves
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in \(\mathbb{R}^D\)
• On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
• The derivative nonlinear Schrödinger equation on the half line
• Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
• Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
• The Cauchy problem for the Benjamin-Ono equation in \(L^{2}\) revisited
• Low regularity conservation laws for the Benjamin-Ono equation
• Low regularity conservation laws for integrable PDE
• On unconditional well-posedness for the periodic modified Korteweg-de Vries equation
• On well-posedness for the Benjamin-Ono equation
• Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• Algebraic Solitary Waves in Stratified Fluids
• N-Periodic Wave and N-Soliton Solutions of the Modified Benjamin-Ono Equation
• Global Smoothing for the Periodic KdV Evolution
• On quadratic Schrödinger equations in R ¹⁺¹ : a normal form approach
• On the regularization mechanism for the periodic Korteweg-de Vries equation
• Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
• Global well-posedness in <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the periodic Benjamin-Ono equation
• Global Solutions for 3D Quadratic Schrodinger Equations
• Normal forms and quadratic nonlinear Klein-Gordon equations
• On the cauchy problem for the benjamin-ono equation
• Benjamin—Ono-related equations and their solutions
• GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H¹(R)
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• Bounds on the growth of high Sobolev norms of solutions to nonlinear Schroedinger equations on $\mathbb{R}$
• Smoothing for the fractional Schroedinger equation on the torus and the real line
• Internal waves of permanent form in fluids of great depth
• Global solutions for the gravity water waves equation in dimension 3

This page was built for publication: Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle