Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation

DOI10.1016/J.JDE.2023.10.054arXiv2209.14116MaRDI QIDQ6140135

Louise Gassot, Slim Ibrahim, Nicolas Camps

Publication date: 19 January 2024

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

Full work available at URL: https://arxiv.org/abs/2209.14116

zbMATH Keywords

nonlinear Schrödinger equationquasilinear equationrandom initial datahalf-wave equationCauchy theoryweakly dispersive equation

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Invariant tori for the cubic Szegö equation
• Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
• Random data Cauchy theory for supercritical wave equations. II. A global existence result
• Random data Cauchy theory for supercritical wave equations I: Local theory
• 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]
• A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• Traveling waves for the cubic Szegő equation on the real line
• Effective integrable dynamics for a certain nonlinear wave equation
• Transverse stability of line soliton and characterization of ground state for wave guide Schrödinger equations
• The cubic Szegő flow at low regularity
• Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian
• Global well-posedness for the derivative nonlinear Schrödinger equation
• Concerning the pathological set in the context of probabilistic well-posedness
• Unbounded Sobolev trajectories and modified scattering theory for a wave guide nonlinear Schrödinger equation
• Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
• MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
• ON THE WAVE EQUATION WITH QUADRATIC NONLINEARITIES IN THREE SPACE DIMENSIONS
• The cubic Szegő equation
• Remarks on Nonlinear Smoothing under Randomization for the Periodic KdV and the Cubic Szegö Equation
• Almost Sure Local Well-Posedness for a Derivative Nonlinear Wave Equation
• Fractional Partial Differential Equations and Their Numerical Solutions
• An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
• Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations
• The cubic szego equation and hankel operators
• Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations
• Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three
• Unbounded Hankel operators and the flow of the cubic Szegő equation
• Pathological Set of Initial Data for Scaling-Supercritical Nonlinear Schrödinger Equations

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