2021 Fiscal Year Annual Research Report
New perspectives on space-time estimates for dispersive equations
| Project/Area Number |
19H01796
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| Research Institution | Saitama University |
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Principal Investigator |
BEZ NEAL 埼玉大学, 理工学研究科, 教授 (30729843)
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| Co-Investigator(Kenkyū-buntansha) |
杉本 充 名古屋大学, 多元数理科学研究科, 教授 (60196756)
中村 昌平 大阪大学, 大学院理学研究科, 助教 (30896121)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | Strichartz estimate / Orthonormal system / Pointwise convergence |
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| Outline of Annual Research Achievements |
Regarding the main goal of developing a fuller theory of Strichartz estimates for orthonormal systems of initial data, progress is ongoing. The focus has been mostly on certain boundary cases which were left open in previous work. In addition, progress is being made on extending the known results regarding Carleson's problem for fermions.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Work towards the main goals of the research project is successfully moving forward. In addition, new research directions which have emerged during the course of the project, such as Carleson's problem for fermions, are also being fruitfully pursued. It should be said though that the effect of the pandemic has been felt in the sense that it is significantly more challenging to conduct deep research discussions with collaborators.
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| Strategy for Future Research Activity |
It is planned to continue work towards the main goals of the original reseach proposal and establish a satisfactory theory of Strichartz estimates for orthonormal systems. Work will also be carried out on Carleson's problem for fermions and it is expected that these projects can be completed in the short to medium term.
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