New Frontiers in Kinetic Equation Theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 26887008
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Mathematical analysis
• Research Institution: Saitama University
• Principal Investigator: BEZ Neal 埼玉大学, 研究機構研究企画推進室, 准教授 (30729843)
• Research Collaborator: Bennett Jonathan University of Birmingham ; Gutierrez Susana University of Birmingham ; Jeavons Chris Waseda University ; Lee Sanghyuk Seoul National University ; Machihara Shuji Saitama University ; Ozawa Tohru Waseda University ; Saito Hiroki Kogakuin University ; Sugimoto Mitsuru Nagoya University
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: 運動輸送方程式 / 分散型方程式 / 波動方程式 / 時空間評価式

Outline of Final Research Achievements

Significant progress on the fundamental theory of the kinetic transport equation has been obtained through the use of techniques from harmonic analysis. In particular, techniques developed in connection with the Fourier restriction conjecture were applied. Additionally, using similar techniques, this research has also pushed forward the theory of another class of equations, including the Schrodinger equation from quantum mechanics and the wave equation from classical physics.

To foster greater interaction between partial differential equations research with harmonic analysis and geometric analysis, an international conference was organised at Saitama University. The conference was a great success, and was the catalyst for new developments in several important research topics.

Free Research Field

偏微分方程式