Real analysis and numerical compitaion to the fluid equations

• Project/Area Number: 25870004
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis; Basic analysis
• Research Institution: Tokyo Institute of Technology (2014-2015); Hokkaido University (2013)
• Principal Investigator: Yoneda Tsuyoshi 東京工業大学, 大学院理工学研究科, 准教授 (30619086)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: Navier-Stokes方程式 / Euler方程式 / Green関数 / 剥離現象 / 軸対称Navier-Stokes方程式 / 軸対称Euler方程式 / グリーン関数 / 等角写像 / 渦度方程式 / 特性曲線法 / 微分幾何学 / 有限要素法 / Taylor-Green渦

Outline of Final Research Achievements

We used incompressible Navier-Stokes and incompressible Euler equations to analyze local behavior of the particle trajectory on these flows. Also we implemented the numerical computation. More precisely, we focused on the hyperbolic flow configuration, swirl and no-slip boundary, and see how these behavior affect the flow behavior themselves. In particular, we studied time evolution of the maximum value and its position of the Navier-Stokes flow, separation phenomena of the Navier-Stokes flow with the no-slip boundary, and the ralation between boundary shape and the hyperbolic flow configuration of the Euler flow.

Research Products

• [Journal Article] A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary (2016)
  • Author(s): P-Y. Hsu, H. Notsu, T. Yoneda
  • Journal Title: J. Fluid Mech Volume: 794 Pages: 444-459
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] An ODE for boundary layer separation on a sphere and a hyperbolic space (2014)
  • Author(s): C-H. Chan, M. Czubak and T. Yoneda
  • Journal Title: Physica D Volume: 282 Pages: 34-38
  • NAID: 120006459736
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Resonant interaction of Rossby waves in two-dimensional flow on a β plane (2013)
  • Author(s): M. Yamada and T. Yoneda
  • Journal Title: Physica D Volume: 245
  • NAID: 120006466474
  • Peer Reviewed
• [Journal Article] On the Liouville theorem for the stationary Navier-Stokes equations in a critical space (2013)
  • Author(s): D. Chae and T. Yoneda
  • Journal Title: J. Math. Anal. Appl Volume: 405
  • NAID: 120006459676
  • Peer Reviewed
• [Journal Article] Streamlines concentration and application to the incompressible Navier-Stokes equations, (2013)
  • Author(s): E. Foxall, S. Ibrahim and T. Yoneda
  • Journal Title: Tohoku Math. J Volume: 65
  • NAID: 130005562141
  • Peer Reviewed
• [Journal Article] Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data (2013)
  • Author(s): S.Ibrahim and T. Yoneda
  • Journal Title: J. Math. Sci. Univ. Tokyo Volume: 20
  • NAID: 120005678231
  • Peer Reviewed
• [Journal Article] On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space (2013)
  • Author(s): C-H Chan and T. Yoneda
  • Journal Title: Dynamics of PDE Volume: 10
  • NAID: 120006459719
  • Peer Reviewed
• [Presentation] Loss of continuity of the solution map for the Euler equations in \alpha-modulation spaces including B^1_{\infty, 1} and C^{1+s} (0＜s＜1) (2015)
  • Author(s): T. Yoneda
  • Organizer: 第7回 名古屋微分方程式研究集会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2015-03-03 – 2015-03-05
  • Invited
• [Presentation] A differential geometric consideration on the Navier-Stokes flow and its numerical computation (2014)
  • Author(s): T. Yoneda
  • Organizer: Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics
  • Place of Presentation: ホテル日航奈良、奈良県
  • Invited
• [Presentation] Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions (2013)
  • Author(s): T. Yoneda
  • Organizer: PRIMA Congress Shanghai
  • Place of Presentation: Shanghai Jiao Tong University, China
  • Invited
• [Presentation] Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions (2013)
  • Author(s): T. Yoneda
  • Organizer: RIMS 研究集会（調和解析と偏微分方程式）
  • Place of Presentation: 京都大学数理解析研究所、京都市
  • Invited
• [Presentation] Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions (2013)
  • Author(s): T. Yoneda
  • Organizer: Fourth Japan-China Workshop on Mathematical Topics from Fluid Mechanics
  • Place of Presentation: 東京工業大学、目黒区
  • Invited