波导上散焦三次Schrödinger方程的全局适定性和散射ℝ2×𝕋2.

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-05-24 DOI:10.1142/S0219891619500048

Zehua Zhao

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引用次数: 7

摘要

我们在[公式：见正文]上考虑散焦三次非线性薛定谔方程的大数据散射问题。该方程在能量和质量水平上都是至关重要的。关键成分是全局时间Stricharz估计、共振系统近似、轮廓分解和能量诱导方法。假设二维三次谐振系统存在大数据散射，我们证明了该问题的大数据散射。这个问题是Hani和Pausader研究的一个问题的三次类似。

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Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2

We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on [Formula: see text]. This equation is critical both at the level of energy and mass. The key ingredients are global-in-time Stricharz estimate, resonant system approximation, profile decomposition and energy induction method. Assuming the large data scattering for the 2d cubic resonant system, we prove the large data scattering for this problem. This problem is the cubic analogue of a problem studied by Hani and Pausader.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.