On scattering asymptotics for the 2D cubic resonant system

Yang, Kailong; Zhao, Zehua

doi:10.1016/j.jde.2022.11.056

Cited by 7 publications

(2 citation statements)

References 31 publications

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“…After that, this conjecture was confirmed by Cheng-Guo-Zhao [11]. Similarly, Yang-Zhao [42] showed the global well-posedness and scattering of the defocusing, cubic resonant Schrödinger system on R 2 × Z, and using this result, Chen-Guo-Yang-Zhao [10] proved the global well-posedness and scattering of the defocusing cubic NLS (1.16) on R 2 × T. Also, the corresponding results for the cubic NLS on R 2 × T 2 are obtained in Yang-Zhao [43] and Zhao [45]. In the case (d, n, σ) = (3, 1, 2), (4, 1, 1) with λ = +1, Zhao [46] obtained the scattering result.…”

Section: Nls On the Wave Guide Manifoldsmentioning

confidence: 67%

Small data finite-time blow-up solutions for the nonlinear Schrödinger equation in general dimensions

Kawakami¹

2023

DCDS

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We consider 3-dimensional nonlinear Schrödinger equation with an averaged nonlinearity. This is a generalized model of the resonant system of NLS with partial harmonic oscillator, in terms of the nonlinear power. We give a new proof for the conservation law of Kinetic energy and remove a restriction on the nonlinearity. Moreover, in the focusing, super-quintic, and sub-nonic case, we construct a ground state solution and classify the behavior of the solutions below the ground state. We show the sharp threshold for scattering and blow up.

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Section: Nls On the Wave Guide Manifoldsmentioning

confidence: 67%

Small data finite-time blow-up solutions for the nonlinear Schrödinger equation in general dimensions

Kawakami¹

2023

DCDS

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“…A new bilinear estimate on T 3 will therefore be proved in order to obtain a proper estimate for the cubic potential, and we refer to Lemma 3.2 for details. For interested readers, we also refer to [7,8,14,15,16,17,29,30,32,34,35,36] for further well-posedness results for NLS (with single nonlinear potential) on tori or waveguide manifolds based on the atomic space theory. (See [24,31] for other dispersive equations on waveguides.)…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On well-posedness results for the cubic-quintic NLS on $\mathbb{T}^3$

Luo¹,

Yu²,

Yue³

et al. 2023

Preprint

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We consider the periodic cubic-quintic nonlinear Schrödinger equationon the three-dimensional torus T 3 with µ 1 , µ 2 ∈ R \ {0}. As a first result, we establish the small data well-posedness of (CQNLS) for arbitrarily given µ 1 and µ 2 . By adapting the crucial perturbation arguments in [33] to the periodic setting, we also prove that (CQNLS) is always globally well-posed in H 1 (T 3 ) in the case µ 2 > 0.

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On Scattering for Critical NLS on Waveguide Manifolds: A Short Survey

Yu,

Zhao

2024

Trends in Mathematics

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On scattering asymptotics for the 2D cubic resonant system

Cited by 7 publications

References 31 publications

Small data finite-time blow-up solutions for the nonlinear Schrödinger equation in general dimensions

Small data finite-time blow-up solutions for the nonlinear Schrödinger equation in general dimensions

On well-posedness results for the cubic-quintic NLS on $\mathbb{T}^3$

On Scattering for Critical NLS on Waveguide Manifolds: A Short Survey

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