Long Time Dynamics for Defocusing Cubic Nonlinear Schrödinger Equations on Three Dimensional Product Space

Z Zhao, J Zheng - SIAM Journal on Mathematical Analysis, 2021 - SIAM
In this article, we study long time dynamics for defocusing cubic nonlinear Schrödinger
equations (NLS) on three dimensional product space. First, we apply the decoupling method …

On bilinear Strichartz estimates on waveguides with applications

Y Deng, C Fan, K Yang, Z Zhao, J Zheng - Journal of Functional Analysis, 2024 - Elsevier
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Global Well-posedness for the Focusing Cubic NLS on the Product Space

X Yu, H Yue, Z Zhao - SIAM Journal on Mathematical Analysis, 2021 - SIAM
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear
Schrödinger equation on the product space R*T^3 with initial data below the threshold that …

On Existence and Stability Results for Normalized Ground States of Mass-Subcritical Biharmonic Nonlinear Schrödinger Equation on

H Hajaiej, Y Luo, L Song - SIAM Journal on Mathematical Analysis, 2024 - SIAM
We study the focusing mass-subcritical biharmonic nonlinear Schrödinger equation (BNLS)
on the product space. Following the crucial scaling arguments introduced in [Terracini …

On long time behavior of the focusing energy-critical NLS on Rd× T via semivirial-vanishing geometry

Y Luo - Journal de Mathématiques Pures et Appliquées, 2023 - Elsevier
We study the focusing energy-critical NLS (NLS) i∂ t u+ Δ x, yu=−| u| 4 d− 1 u on the
waveguide manifold R xd× T y with d≥ 2. We reveal the somewhat counterintuitive …

On scattering asymptotics for the 2D cubic resonant system

K Yang, Z Zhao - Journal of Differential Equations, 2023 - Elsevier
In this paper, we prove scattering asymptotics for the 2D (discrete dimension) cubic resonant
system. This scattering result was used in Zhao [38] as an assumption to obtain the …

Global well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds

X Yu, H Yue, Z Zhao - SIAM Journal on Mathematical Analysis, 2024 - SIAM
In this paper, we study the well-posedness theory and the scattering asymptotics for fourth-
order Schrödinger equations (4NLS) on waveguide manifolds (semiperiodic spaces),,. The …

Sharp scattering for focusing intercritical NLS on high-dimensional waveguide manifolds

Y Luo - Mathematische Annalen, 2024 - Springer
We study the focusing intercritical NLS NLS i∂ tu+ Δ x, yu=-| u| α u on the semiperiodic
waveguide manifold R xd× T y with d≥ 5 and α∈(4 d, 4 d-1). In the case d≤ 4, with the aid …

On the focusing fractional nonlinear Schr\"{o} dinger equation on the waveguide manifolds

A Esfahani, H Hajaiej, Y Luo, L Song - arxiv preprint arxiv:2305.19791, 2023 - arxiv.org
In this paper, we consider the focusing fractional nonlinear Schr\"{o} dinger equation (FNLS)
on the waveguide manifolds $\mathbb {R}^ d\times\mathbb {T}^ m $ both in the isotropic and …

A Legendre–Fenchel Identity for the Nonlinear Schrödinger Equations on : Theory and Applications

Y Luo - The Journal of Geometric Analysis, 2024 - Springer
The present paper is inspired by a previous work of the author, where the large data
scattering problem for the focusing cubic nonlinear Schrödinger equation (NLS) on R 2× T …