Project/Area Number  10045040 
Research Category 
GrantinAid for Scientific Research (B).

Section  UniversitytoUniversity Cooperative Research 
Research Field 
Engineering fundamentals

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
AOKI Kazuo Kyoto University, Graduate School of Engineering, Professor, 工学研究科, 教授 (10115777)

CoInvestigator(Kenkyūbuntansha) 
GOLSE Franco パリ第7大学, 数学科, 教授
BARDOS Claud パリ第7大学, 数学科, 教授
ASANO Kiyoshi Kyoto University, Graduate School of Human and Environmental Studies, Professor, 人間環境学研究科, 教授 (90026774)
TAKATA Shigeru Kyoto University, Graduate School of Engineering, Associate Professor, 工学研究科, 助教授 (60271011)
SONE Yoshio Kyoto University, Graduate School of Engineering, Professor Emeritus, 工学研究科, 名誉教授 (80025923)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥4,400,000 (Direct Cost : ¥4,400,000)
Fiscal Year 2000 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1999 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1998 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  Boltzmann equation / Euler equation / boundarylayer equation / Liouville equation / Knudsen layer / rarefied gas flows / flow bifurcation / flow stability / ボルツマン方程式 / オイラー方程式 / 境界層方程式 / リュービル方程式 / クヌーセン層 / 希薄気流 / 流れの分岐 / 流れの安定性 / 多成分混合気体 / 速度分布関数 / 輸送方程式 / 希薄化効果 
Research Abstract 
1. With the help of the French group (FG), the Japanese group (JG) has established the asymptotic theory (the fluiddynamic equations, the slip boundary conditions, and the Knudsenlayer corrections near the boundary) describing the general behavior of slightly rarefied gas flows with finite Mach numbers by means of a systematic asymptotic analysis of the Boltzmann equation. This theory also contains the systematic derivation of the viscous boundarylayer equation in fluid dynamics from the Boltzmann equation. The results inspired the mathematical study of FG on the boundarylayer equation. 2. JG and FG have jointly worked on the direct derivation of the fluiddynamic equations (the Euler system of equations) from the manyparticle system (the Liouville equation). Using different approaches, each group has succeeded in the formal derivation. In addition, JG reflected on the formal derivation of the Boltzmann equation from the manyparticle system and provided FG with a clear and systema
… More
tic derivation. This leads to a possibility of a new mathematical proof of the derivation of the Boltzmann equation. 3. Cooperating with FG, JG investigated the rarefied gas flow induced by the discontinuity in the boundary temperature by means of a numerical analysis and clarified the behavior of the flow for a wide range of gas rarefaction. In this flow, the discontinuity of the molecular velocity distribution function propagates from the boundary into the gas. As the first step of mathematical study, on the basis of a linear transport equation that possesses a similar property to the Boltzmann equation concerning the propagation of discontinuity but has a much simpler structure, JG and FG jointly analyzed, with mathematical rigor, the propagation of discontinuity in the medium. 4. JG constructed a systematic theory for the kinetic solution scheme of the general conservation equations including fluiddynamic equations (e.g., the standard Euler and NavierStokes equations) and provided FG with the theory for further mathematical study. In addition, JG, with the help of FG, succeeded in obtaining mathematically rigorous bounds of the boundary conditions for the fluiddynamic equations on the interface where evaporation or condensation is taking place. 5. JG provided FG with the system of fluiddynamic type equations that describe the ghost effect for gaseous mixtures, and FG investigated its mathematical properties. Less
