On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation

DOI10.1137/22m1531063arXiv2011.12925OpenAlexW3107800228MaRDI QIDQ6195321

Xueying Yu, Haitian Yue

Publication date: 13 March 2024

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.12925

zbMATH Keywords

nonlinear Schrödinger equationglobal well-posednesscompact manifold

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions
• The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
• Global well-posedness of the energy-critical defocusing NLS on \({\mathbb{R} \times \mathbb{T}^3}\)
• Global well-posedness of the energy-critical defocusing NLS on rectangular tori in three dimensions.
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Well-posedness and scattering for nonlinear Schrödinger equations on \(\mathbb{R}^d \times \mathbb{T}\) in the energy space
• Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
• Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
• Modified scattering for the cubic Schrödinger equation on product spaces: the nonresonant case
• Scale-invariant Strichartz estimates on tori and applications
• Global regularity for the energy-critical NLS on \(\mathbb S^3\)
• On scattering for the defocusing nonlinear Schrödinger equation on waveguide \(\mathbb{R}^m \times \mathbb{T}\) (when \(m = 2, 3)\)
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• The growth in time of higher Sobolev norms of solutions to Schrödinger equations on compact Riemannian manifolds
• Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori
• 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]
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Existence of solutions for Schrödinger evolution equations
• Smoothing properties and retarded estimates for some dispersive evolution equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• On a bilinear Strichartz estimate on irrational tori
• Energy and local energy bounds for the 1-d cubic NLS equation in \(H^{-\frac{1}{4}}\)
• A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds
• On the global well-posedness of energy-critical Schrödinger equations in curved spaces
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\)
• Global well-posedness and scattering for the defocusing \(\dot{H}^{1/2}\)-critical nonlinear Schrödinger equation in \(\mathbb{R}^2\)
• The proof of the \(l^2\) decoupling conjecture
• Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Strichartz estimates for the Schrödinger equation on irrational tori
• Strichartz estimates for partially periodic solutions to Schrödinger equations in \(4d\) and applications
• Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D
• On the blow up phenomenon of the critical nonlinear Schrödinger equation
• Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\)
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T²
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• Strichartz estimates for Schrödinger equations on irrational tori
• MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• Bilinear virial identities and applications
• Tensor products and correlation estimates with applications to nonlinear Schrödinger equations
• Endpoint Strichartz estimates
• Description of the lack of compactness for the Sobolev imbedding
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
• On nonlinear schrödinger equations
• Dispersive estimates for principally normal pseudodifferential operators
• Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ³
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$
• Nonlinear Schrödinger equation on four-dimensional compact manifolds
• Global Well-Posedness of the Cubic Nonlinear Schrödinger Equation on Closed Manifolds
• Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2
• Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
• Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2
• Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations
• On the defect of compactness for the Strichartz estimates of the Schrödinger equations

This page was built for publication: On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation