Probabilistic local wellposedness of 1D quintic NLS below \(L^2(\mathbb{R})\)

DOI10.1016/J.JMAA.2023.127195zbMath1530.35282OpenAlexW4323657788MaRDI QIDQ6110850

Gyeongha Hwang, Haewon Yoon

Publication date: 6 July 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2023.127195

zbMATH Keywords

nonlinear Schrödinger equationbilinear Strichartz estimateprobabilistic wellposedness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
• Random data Cauchy theory for supercritical wave equations I: Local theory
• A smoothing property for the \(L^2\)-critical NLS equations and an application to blowup theory
• Random data Cauchy problem for supercritical Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• A sharp bilinear restriction estimate for paraboloids
• A remark on norm inflation for nonlinear Schrödinger equations
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities
• Probabilistic well-posedness of the mass-critical NLS with radial data below \(L^2(\mathbb{R}^d)\)
• On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^{𝕕}, 𝕕≥3
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• Probabilistic well-posedness of generalized KdV
• Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS

This page was built for publication: Probabilistic local wellposedness of 1D quintic NLS below \(L^2(\mathbb{R})\)