New developments on the restriction conjecture for the Fourier transform using multilinear analysis

使用多线性分析傅立叶变换限制猜想的新进展

• 批准号: 18F18020
• 负责人: BEZ NEAL
• 金额: $ 0.96万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-04-25 至 2020-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18F18020/
• 关键词: Kinetic transport; Velocity average; Strichartz estimate; Wave equation; Strichartz estimates; Smoothing estimates

Based on techniques arising in the restriction theory of the Fourier transform, several new results were obtained concerning the kinetic transport equation and the wave equation. For the kinetic transport equation, in the case where the velocities belong to the sphere and radially symmetric square-integrable initial data, sharp results were obtained for mixed-norm estimates on velocity averages in the framework of hyperbolic Sobolev spaces. In a different direction, the Keel-Tao approach was used to obtain new inhomogeneous Strichartz estimates of weak type for the wave equation where the so-called acceptability condition fails.

基于傅里叶变换的限制理论中出现的技术，获得了关于动力学输运方程和波动方程的几个新结果。对于动力学输运方程，在速度属于球面和径向对称平方可积初始数据的情况下，在双曲Sobolev空间的框架下，得到了速度平均的混合范数估计的精确结果.在另一个方向上，Keel-Tao方法被用来获得新的非齐次的弱型的波动方程的可接受性条件失败。

项目成果

Smoothing estimates for velocity averages with radial data

使用径向数据平滑估计速度平均值

• 发表时间: 2019
• 期刊: RIMS Kokyuroku Bessatsu
• 作者: Neal Bez;Jayson Cunanan
• 通讯作者: Jayson Cunanan

Smoothing estimates for the kinetic transport equation at critical regularity

临界规律下动力学输运方程的平滑估计

• 发表时间: 2018
• 作者: Bez Neal;Cunanan Jayson;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan
• 通讯作者: Jayson Cunanan

Inhomogeneous Strichartz estimates in some critical cases

某些关键情况下的非齐次 Strichartz 估计

• DOI: 10.1090/proc/14874
• 发表时间: 2020
• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: Neal Bez;Jayson Cunanan;Sanghyuk Lee
• 通讯作者: Sanghyuk Lee

Inhomogeneous Strichartz estimates for some critical cases

对某些关键情况的非齐次 Strichartz 估计

• 发表时间: 2019
• 作者: Bez Neal;Cunanan Jayson;Jayson Cunanan
• 通讯作者: Jayson Cunanan

Inhomogeneous Strichartz estimates for the wave and Schrodinger equations

波方程和薛定谔方程的非齐次 Strichartz 估计

• 发表时间: 2018
• 作者: Bez Neal;Cunanan Jayson;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan;Jayson Cunanan
• 通讯作者: Jayson Cunanan