Research of Harmonic analysis and Partial differential equations

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K20919
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis; Mathematical analysis
• Research Institution: Shinshu University
• Principal Investigator: Yohei Tsutsui 信州大学, 学術研究院理学系, 助教 (40722773)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: Sparse bound / Navier-Stokes equations

Outline of Final Research Achievements

The result in Harmonic analysis we obtained is a sparse bound for an operator related to the maximal Riesz means. The maximal operator is deeply connected to the Kakeya conjecture. The method of sparse bound is recently developed.
The results in PDEs we obtained mainly are related to incompressible Navier-Stokes equations. Using techniques in Harmonic analysis, we gave estimates of the solutions. Moreover, we analyzed the Stokes operator on domains that do not satisfy a condition.

Free Research Field

実解析学

Academic Significance and Societal Importance of the Research Achievements

実解析的研究で得られた結果については、さらなる発展が不可欠ではあるが、sparse bound を用いた Kakeya 予想への貢献への第1歩であると考えている。
偏微分方程式での結果について： Naiver-Stokes 方程式は大気などの動きを記述する方程式であるため、その解の様々な情報は、風力発電、天気予報などの分野で有益である。