New perspectives on space-time estimates for dispersive equations

2022 Fiscal Year Final Research Report

• Project/Area Number: 19H01796
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Saitama University
• Principal Investigator: Bez Neal 埼玉大学, 理工学研究科, 教授 (30729843)
• Co-Investigator(Kenkyū-buntansha): 中村 昌平 大阪大学, 大学院理学研究科, 助教 (30896121) ; 杉本 充 名古屋大学, 多元数理科学研究科, 教授 (60196756)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: Strichartz estimates / Orthonormal systems / Fermions / Pointwise convergence

Outline of Final Research Achievements

A key outcome of this research project was the successful development of the theory of Strichartz estimates for orthonormal systems of initial data. In particular, significant progress has been made in the case of the wave equation, the Klein-Gordon equation, and the fractional Schrodinger equations. The first step was to establish certain oscillatory integral estimates with appropriate weights, and these estimates were combined with ideas of Frank-Sabin to obtain the Strichartz estimates for orthonormal initial data. Additionally, this research project initiated the study of Carleson's pointwise convergence problem for infinitely many fermions and significant progress was made in the one-dimensional case. This was achieved by first establishing orthonormal Strichartz estimates for fractional Schrodinger equations in a certain boundary case. It is expected that this paper will inspire further research in this direction.

Free Research Field

調和解析

Academic Significance and Societal Importance of the Research Achievements

本研究は、無限個の粒子に対する分散型偏微分方程式の理論に重要な貢献を果たす。このような方程式はさまざまな物理現象をモデル化しており、本研究は将来的にも応用されることが期待される。

調和解析および偏微分方程式論の研究交流をさらに推進するために、5日間の国際的な学会を ICMS (エディンバラ) で開催した。