Mathematical analysis of nonlinear partial differential equations related with vorticity fields of viscous incompressible flows

• Project/Area Number: 20840033
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: MAEKAWA Yasunori Kyushu University, 大学院・理学研究科, 講師 (70507954)
• Project Period (FY): 2008 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,237,000 (Direct Cost: ¥2,490,000、Indirect Cost: ¥747,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥1,677,000 (Direct Cost: ¥1,290,000、Indirect Cost: ¥387,000)
• Keywords: 偏微分方程式 / 流体力学 / 非圧縮性粘性流体 / Navier-Stokes方程式 / 渦度方程式 / Burgers渦 / 安定性解析 / 非線形偏微分方程式 / 渦度場 / 自己相似解

Research Abstract

It is well-known that vorticity fields play important roles in dynamics of incompressible flows. This research aims to analyze linear and nonlinear partial differential equations related with vorticity fields mathematically. As one of the results obtained in this research, it is rigorously proved that some stationary solutions which are known as a model of a coherent structure of vortex tubes in turbulent flows are asymptotically stable with respect to small three-dimensional perturbation flows. This research has successfully made an important contribution in the theory of partial differential equations and the study of the dynamics of turbulent flows.

Research Products

• [Journal Article] Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations (2009)
  • Author(s): Maekawa, Y.
  • Journal Title: Mathematical Models and Methods in Applied Sciences 19 Pages: 669-705
  • NAID: 120006459597
  • Peer Reviewed
• [Journal Article] On the existence of Burgers vortices for high Reynolds numbers (2009)
  • Author(s): Maekawa, Y
  • Journal Title: Journalof Mathematical Analysis and Applications 349 Pages: 181-200
  • NAID: 120006459548
  • Peer Reviewed
• [Journal Article] Mathematical approach to asymmetric Burgers vortices at large circulations (2009)
  • Author(s): 前川泰則
  • Journal Title: 数理解析研究所講究録1642オイラー方程式の数理:渦運動150年 Pages: 43-52
• [Journal Article] On the existence of Burgers vortices for high Reynolds numbers (2009)
  • Author(s): Yasunori Maekawa
  • Journal Title: Journal of Mathematical Analysis and Applications 349 Pages: 181-200
  • NAID: 120006459548
  • Peer Reviewed
• [Journal Article] A lower bound for fundamental solutions of the heat convection equations (2008)
  • Author(s): Maekawa, Y.
  • Journal Title: Archive for Rational Mechanics and Analysis 189no.1 Pages: 45-58
  • NAID: 120006459492
  • Peer Reviewed
• [Journal Article] On spatial decay estimates for derivatives of vorticities with application to large time behavior of the two dimensional Navier-Stokes flow (2008)
  • Author(s): aekawa, Y.
  • Journal Title: Journal of Mathematical Fluid Mechanics. 10no.1 Pages: 89-105
  • Peer Reviewed
• [Presentation] Three dimensional stability of the axisymmetric Burgers vortex (2010)
  • Author(s): Yasunori Maekawa
  • Organizer: International Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: Waseda University
• [Presentation] Three dimensional stability of the axisymmetric Burgers vortex (2010)
  • Author(s): 前川泰則
  • Organizer: International Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学(東京都)
• [Presentation] Stability of the axisymmetric Burgers vortex (2009)
  • Author(s): Yasunori Maekawa
  • Organizer: Mathematical Analysis on the Navier-Stokes Equations and Reralted Topics, Past and Future-In memory of Professor Tetsuro Miyakawa
  • Place of Presentation: Kobe University
• [Presentation] Burgers渦の安定性に関する数学解析 (2009)
  • Author(s): 前川泰則
  • Organizer: RIMS研究集会オイラー方程式の数理:渦運動と音波150年
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Stability of the axisymmetric Burgers vortex (2009)
  • Author(s): 前川泰則
  • Organizer: RIMS研究集会流体と気体の数学解析
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2009)
  • Author(s): 前川泰則
  • Organizer: 奈良女子大学偏微分方程式研究集会
  • Place of Presentation: 奈良女子大学
• [Presentation] Burgers渦の3次元摂動に対する安定性について (2009)
  • Author(s): 前川泰則
  • Organizer: 若手による流体力学の基礎方程式研究集会
  • Place of Presentation: 名古屋大学
• [Presentation] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2009)
  • Author(s): 前川泰則
  • Organizer: 奈良女子大学偏微分方程式研究集会
  • Place of Presentation: 奈良女子大学(奈良県)
• [Presentation] Three dimensional stability of the Burgers vortex (2009)
  • Author(s): 前川泰則
  • Organizer: 流体と気体の数学解析
  • Place of Presentation: 京都大学数理解析研究所(京都府)
• [Presentation] Burgers渦の安定性に関する数学解析 (2009)
  • Author(s): 前川泰則
  • Organizer: オイラー方程式の数理:渦運動と音波150年
  • Place of Presentation: 京都大学数理解析研究所(京都府)
• [Presentation] Stability of the axisymmetric Burgers vortex (2009)
  • Author(s): 前川泰則
  • Organizer: Mathematical Analysis on the Navier-Stokes Equations and Related Topics, Past and Future-In memory of Professor Tetsuro Miyakawa
  • Place of Presentation: 神戸大学(兵庫県)
• [Presentation] Asymmetric Burgers vortices at large circulations (2008)
  • Author(s): Yasunori Maekawa
  • Organizer: Workshop Mathematical Fluid Dynamics
  • Place of Presentation: ダルムシュタッド工科大学(ドイツ)
  • Year and Date: 2008-09-09
• [Presentation] Mathematical approach to asymmetric Burgers vortices at large circulations (2008)
  • Author(s): 前川 泰則
  • Organizer: 渦運動150年
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-07-16
• [Presentation] On a free boundary problem of the coupled Navier-Stokes/mean curvature equations (2008)
  • Author(s): 前川 泰則
  • Organizer: パターンダイナミクスの数理とその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-06-25
• [Presentation] Stability of the Burgers vortex (2008)
  • Author(s): 前川泰則
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学
• [Presentation] Asymmetric Burgers vortices at large circulation (2008)
  • Author(s): Yasunori Maekawa
  • Organizer: Workshop Mathemtical Fluid Dynamics
  • Place of Presentation: Technische Universitat Darmstadt
• [Presentation] Mathematical approach to asymmetric Burgers vortices at large circulations (2008)
  • Author(s): Yasunori Maekawa
  • Organizer: RIMS研究集会渦運動150年
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] On a free boundary problem of the coupled Navier-Stokes / mean curvature equations (2008)
  • Author(s): Yasunori Maekawa
  • Organizer: RIMS研究集会パターンダイナミクスの数理とその周辺
  • Place of Presentation: 京都大学数理解析研究所