On bilinear Strichartz estimates on waveguides with applications
DOI10.1016/j.jfa.2024.110595zbMATH Open1546.35176MaRDI QIDQ6592090
Chenjie Fan, Yangkendi Deng, Kailong Yang, Ji Qiang Zheng, Zehua Zhao
Publication date: 24 August 2024
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
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- The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
- Global well-posedness of the energy-critical defocusing NLS on \({\mathbb{R} \times \mathbb{T}^3}\)
- 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 \(H^1(\mathbb T^3)\)
- Scale-invariant Strichartz estimates on tori and applications
- On scattering for the defocusing nonlinear Schrödinger equation on waveguide \(\mathbb{R}^m \times \mathbb{T}\) (when \(m = 2, 3)\)
- 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]
- Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- A sharp bilinear restriction estimate for paraboloids
- On a bilinear Strichartz estimate on irrational tori
- Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
- Global endpoint Strichartz estimates for Schrödinger equations on the cylinder \(\mathbb{R} \times \mathbb{T}\)
- On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\)
- Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces
- On scattering asymptotics for the 2D cubic resonant system
- Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
- On global-in-time Strichartz estimates for the semiperiodic Schrödinger equation
- The proof of the \(l^2\) decoupling conjecture
- Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
- Strichartz estimates for partially periodic solutions to Schrödinger equations in \(4d\) and applications
- Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D
- Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\)
- Global Well-Posedness for Schrödinger Equations with Derivative
- Periodic Nonlinear Schrödinger Equation in Critical $H^{s}(\mathbb{T}^n)$ Spaces
- 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 $d ≥3$
- MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
- Mass concentration phenomena for the $L^2$-critical nonlinear Schrödinger equation
- A bilinear approach to the restriction and Kakeya conjectures
- Endpoint Strichartz estimates
- Long Time Dynamics for Defocusing Cubic Nonlinear Schrödinger Equations on Three Dimensional Product Space
- On Scattering for the Defocusing Quintic Nonlinear Schrödinger Equation on the Two-Dimensional Cylinder
- 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
- On 2D nonlinear Schrödinger equations with data on \(\mathbb{R} \times \mathbb{T}\)
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