Probabilistic well-posedness of the mass-critical NLS with radial data below \(L^2(\mathbb{R}^d)\)

DOI10.1016/J.JMAA.2019.03.058zbMath1416.35240OpenAlexW2931032284MaRDI QIDQ2633827

Gyeongha Hwang

Publication date: 10 May 2019

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.2019.03.058

zbMATH Keywords

nonlinear Schrödinger equationStrichartz estimatesradial dataalmost sure well-posednessmass-critical nonlinearity

Mathematics Subject Classification ID

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)

Related Items (2)

Probabilistic local wellposedness of 1D quintic NLS below \(L^2(\mathbb{R})\) ⋮ Probabilistic Cauchy theory for the mass-critical fourth-order nonlinear Schrödinger equation

Cites Work

• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Random data Cauchy theory for the generalized incompressible Navier-Stokes equations
• Random data Cauchy theory for supercritical wave equations I: Local theory
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Random data Cauchy problem for supercritical Schrödinger equations
• Invariant measures for the Gross-Pitaevskii equation
• Invariant measures for the 2D-defocusing nonlinear Schrödinger 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 \(5\)
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities
• Probabilistic well-posedness for the cubic wave equation
• Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case
• 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
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³
• Endpoint Strichartz estimates
• Probabilistic well-posedness of generalized KdV
• 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
• Strichartz estimates in spherical coordinates
• Almost sure scattering for the energy-critical NLS with radial data below H1(R4)
• Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on \(\mathbb R^3\)

This page was built for publication: Probabilistic well-posedness of the mass-critical NLS with radial data below \(L^2(\mathbb{R}^d)\)