Computer-assisted solution verification for the Navier-Stokes equation with large Reynolds numbers

2023 Fiscal Year Final Research Report

• Project/Area Number: 20KK0306
• Research Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research (A))
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Tokyo Woman's Christian University (2023); Niigata University (2020-2022)
• Principal Investigator: Xuefeng Liu 東京女子大学, 現代教養学部, 教授 (50571220)
• Project Period (FY): 2021 – 2023
• Keywords: ナビエ・ストークス方程式 / 計算機援用証明 / 固有値問題の厳密評価 / 精度保証付き数値計算 / 非線形偏微分方程式

Outline of Final Research Achievements

This research focuses on analyzing fluids in three-dimensional space using a new computer-assisted proof method. Generally, a higher Reynolds number causes difficulty in studying the involved eigenvalue problem. The research leader collaborated with Professor M. Plum in Germany to develop highly accurate eigenvalue evaluation methods and to verify flows with Reynolds numbers over 100. Additionally, research expenses were used to facilitate exchanges with researchers in Europe and the United States, thereby internationally promoting the achievements of Japan’s research in the field of computer-assisted proof.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

本研究は、流体の動きを中心とした非線形偏微分方程式の解析に対して、精度保証付き数値計算の複数の手法を発展させ、この分野の研究を大きく推進しました。また、日本の研究者と海外の研究者との交流が大変不足している問題点に対して、本研究では、ドイツのM. Plum教授との共同研究、ヨーロッパやアメリカの多くの研究者への訪問、国際研究集会の開催を通じて、国際交流不足の状況を大きく改善することができたと考えています。