Long time behavior of solutions of nonlinear dispersive equations

非线性色散方程解的长时间行为

• 批准号: 15K17570
• 负责人: Roy Tristan
• 金额: $ 2.33万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2015
• 资助国家: 日本
• 起止时间: 2015-04-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15K17570/
• 关键词: dispersive equations; global well-posedness; scattering; local well-posednes; loglog supercritical; local well-posedness; third-order nonlinearity; Dispersive equations; Global existence; Scattering; Schrodinger; Wave, Klein-Gordon; Local well

I worked on several problems. I proved global existence and scattering of nonsmooth solutions of some barely supercritical Schrodinger equations with a defocusing (i.e repulsive) nonlinearity: this lead to a paper recently published in International Mathematics Research Notices. I also proved global existence and scattering of smooth and nonsmooth solutions below ground state of some size-dependent barely supercritical Schrodinger equations with a focusing (i.e attractive) nonlinearity: this lead to a preprint (arXiv:1701.02689). I also worked on a problem with Prof Kotaro Tsugawa (Nagoya University and Chuo University) that involves the construction of local smooth solutions of fully nonlinear equations that satisfya dispersive property in a weak sense. This collaboration is about to lead to a preprint.

我研究了几个问题。我证明了全局存在性和散射的非光滑解的一些勉强超临界薛定谔方程的散焦（即排斥）的非线性：这导致最近发表在国际数学研究通告。我还证明了一些具有聚焦（即吸引）非线性的尺寸依赖的几乎超临界薛定谔方程的基态以下光滑和非光滑解的整体存在性和散射性：这导致了预印本（arXiv：1701.02689）。我还与津川浩太郎教授（名古屋大学和中央大学）合作研究了一个问题，该问题涉及满足弱色散性质的完全非线性方程的局部光滑解的构造。这次合作即将导致一个预印本。

项目成果

On Jensen-type inequalities for unbounded radial scattering solutions of barely supercritical Schrodinger equations

关于准超临界薛定谔方程的无界径向散射解的 Jensen 型不等式

• 发表时间: 2017
• 作者: Thomas Duyckaerts;Tristan Roy;Tristan Roy;Tristan Roy;Tristan Roy;Tristan Roy
• 通讯作者: Tristan Roy

On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrodinger Equation

Loglog能量-超临界薛定谔方程非光滑径向散射解的Jensen型不等式

• DOI: 10.1093/imrn/rny045
• 发表时间: 2018
• 期刊: International Mathematics Research Notices
• 影响因子: 1
• 作者: Setsuro Fujiie;Andre Martinez and Takuya Watanabe;Takafumi Amaba;菅徹;Tristan Roy
• 通讯作者: Tristan Roy

On the asymptotic behavior of solutions of barely supercritical Schrodinger equations with radial data

关于径向数据的准超临界薛定谔方程解的渐近行为

• 发表时间: 2016
• 作者: Thomas Duyckaerts;Tristan Roy;Tristan Roy;Tristan Roy;Tristan Roy;Tristan Roy;Tristan Roy
• 通讯作者: Tristan Roy

Tristan Roy's homepage

特里斯坦·罗伊的主页

Blow-up Of The Critical Sobolev Norm For Nonscattering Radial Solutions Of Supercritical Wave Equations In Space Dimension 3

空间3维超临界波动方程非散射径向解的临界Sobolev范数的放大

• 发表时间: 2017
• 期刊: Bulletin de la SMF
• 作者: Thomas Duyckaerts;Tristan Roy
• 通讯作者: Tristan Roy