Probabilistic well-posedness of generalized KdV

DOI10.1090/proc/13718zbMath1391.35341OpenAlexW2592073597MaRDI QIDQ4590983

Gyeongha Hwang, Chulkwang Kwak

Publication date: 21 November 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13718

zbMATH Keywords

well-posednessgeneralized KdVprobabilistic local smoothing estimate

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (3)

Convergence problem of Ostrovsky equation with rough data and random data ⋮ Probabilistic well-posedness of the mass-critical NLS with radial data below \(L^2(\mathbb{R}^d)\) ⋮ Probabilistic local wellposedness of 1D quintic NLS below \(L^2(\mathbb{R})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Invariance of the Gibbs measure for the periodic quartic gKdV
• On invariant Gibbs measures for the generalized KdV equations
• Well-posedness for the supercritical gKdV equation
• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
• Bilinear local smoothing estimate for Airy equation.
• Global rough solutions to the critical generalized KdV equation
• Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity
• Random data Cauchy theory for the generalized incompressible Navier-Stokes equations
• Random data Cauchy theory for supercritical wave equations I: Local 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
• Periodic nonlinear Schrödinger equation and invariant measures
• Invariant measures for the Gross-Pitaevskii equation
• Global well-posedness and scattering for the defocusing, mass-critical generalized KdV equation
• Two-dimensional nonlinear Schrödinger equation with random radial data
• Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on \(\mathbb R^d\), \(d=4\) and \(5\)
• The supercritical generalized KdV equation: global well-posedness in the energy space and below
• Probabilistic well-posedness for the cubic wave equation
• Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case
• Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^{𝕕}, 𝕕≥3
• Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³
• Remarks on Nonlinear Smoothing under Randomization for the Periodic KdV and the Cubic Szegö Equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation
• Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS
• Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations
• Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on \(\mathbb R^3\)

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