Mathematical analysis for local structures of viscous incompressible flows

• Project/Area Number: 22740090
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kobe University
• Principal Investigator: MAEKAWA Yasunori 神戸大学, 大学院・理学研究科, 准教授 (70507954)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• 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 / 安定性解析 / 解の漸近挙動 / 境界層 / 渦度場 / 非線形偏微分方程式 / 高レイノルズ数 / 粘性零極限 / 基本解の評価 / スケール変換不変性 / 自己相似解 / 線形作用素の半群理論

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. The research in particular has made important contributions in the following topics:
(i) Stability analysis of some stationary solutions modeling vortex tubes in turbulent flows;
(ii) Estimates of fundamental solutions to fractional diffusion equations with a drift;
(iii) Analysis of vorticity equations in the half plane and its applications to inviscid limit problem for the Navier-Stokes equations.

Research Products

• [Journal Article] Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit (2013)
  • Author(s): Maekawa, Y.
  • Journal Title: Advances in Differential Equations Volume: 18 Pages: 101-146
  • NAID: 120006459684
  • Peer Reviewed
• [Journal Article] On nonexistence for stationary solutions to the Navier-Stokes equations with a linear strain (2013)
  • Author(s): P.-Y. Hsu and Y. Maekawa
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 未定 Issue: 2 Pages: 317-333
  • DOI: 10.1007/s00021-012-0114-1
  • Peer Reviewed
• [Journal Article] Long-time asymptotics for two-dimensional exterior flows with small circulation (2013)
  • Author(s): Th. Gallay and Y. Maekawa
  • Journal Title: Analysis and PDE Volume: 未定
  • Peer Reviewed
• [Journal Article] Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift (2013)
  • Author(s): H. Miura and Y. Maekawa
  • Journal Title: Journal of Functional Analysis Volume: 264 Issue: 10 Pages: 2245-2268
  • DOI: 10.1016/j.jfa.2013.02.011
  • NAID: 120006459704
  • Peer Reviewed
• [Journal Article] On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis (2012)
  • Author(s): Kagei, Y. and Maekawa, Y.
  • Journal Title: Journal of Differential Equations Volume: 253 Pages: 2951-2992
  • NAID: 120005039071
  • Peer Reviewed
• [Journal Article] Recent developments in the mathematical analysis of the Burgers vortex (2012)
  • Author(s): Y. Maekawa
  • Journal Title: Gakuto International Series, Mathematical Sciences and Volume: 35 Pages: 103-115
  • Peer Reviewed
• [Journal Article] Recent developments in the mathematical analysis of the Burgers vortex (2012)
  • Author(s): Y.Maekawa
  • Journal Title: Gakuto International Series, Mathematical Sciences and Applications Volume: 35 Pages: 103-115
  • Peer Reviewed
• [Journal Article] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2011)
  • Author(s): Kagei, Y. and Maekawa, Y.
  • Journal Title: Journal of Functional Analysis Volume: 260 Pages: 3036-3096
  • NAID: 120005007645
  • Peer Reviewed
• [Journal Article] Three-dimensional stability of Burgers vortices (2011)
  • Author(s): Gallay, Th. and Maekawa, Y.
  • Journal Title: Communications in Mathematical Physics Volume: 302 Pages: 477-511
  • Peer Reviewed
• [Journal Article] Spectral properties of the linearization at the Burgers vortex in the high rotation limit (2011)
  • Author(s): Maekawa, Y.
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 13 Pages: 515-532
  • Peer Reviewed
• [Journal Article] On Gaussian decay estimates of solutions to some linear elliptic equations and their applications (2011)
  • Author(s): Maekawa, Y.
  • Journal Title: Z. Angew. Math. Phys Volume: 62 Pages: 1-30
  • Peer Reviewed
• [Journal Article] Asymptotic behaviors of solutions to evolution equations in the presenceof translation and scaling invariance (2011)
  • Author(s): Y.Kagei, Y.Maekawa
  • Journal Title: Journal of Functional Analysis Volume: 260 Pages: 3036-3096
  • Peer Reviewed
• [Journal Article] On Gaussian decay estimates of solutions to some linear elliptic equations and their applications (2011)
  • Author(s): Yasunori Maekawa
  • Journal Title: Z.Angew.Math.Phys. Volume: 62 Pages: 1-30
  • Peer Reviewed
• [Journal Article] Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift
  • Author(s): Maekawa, Y. and Miura, H.
  • Journal Title: Journal of Functional Analysis Volume: 受理済み
  • NAID: 120006459704
  • Peer Reviewed
• [Journal Article] Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity
  • Author(s): Gallay, Th. and Maekawa, Y.
  • Journal Title: in Analysis and PDE Volume: 受理済み
  • Peer Reviewed
• [Journal Article] On nonexistence for stationary solutions to the Navier-Stokes equations with a linear strain
  • Author(s): Hsu, P.-Y. and Maekawa, Y.
  • Journal Title: in Journal of Mathematical Fluid Mechanics Volume: 受理済み
  • Peer Reviewed
• [Journal Article] Recent developments in the mathematical analysis of the Burgers vortex
  • Author(s): Yasunori Maekawa
  • Journal Title: Proceeding of 'Mathematical Analysis on the Navier-Stokes equations and Related Topics, Past and Future-in memory of Professor Tetsuro Miyakawa Volume: (印刷中)
  • Peer Reviewed
• [Presentation] On factorization of some second order elliptic operators and its applications (2013)
  • Author(s): Y. Maekawa
  • Organizer: 第30回九州における偏微分方程式研究集会
  • Place of Presentation: 福岡大学
  • Invited
• [Presentation] On the inviscid limit for viscous incompressible flows in the half plane (2013)
  • Author(s): Y. Maekawa
  • Organizer: Geophysical Fluid Dynamics
  • Place of Presentation: Oberwolfach
  • Invited
• [Presentation] Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity (2013)
  • Author(s): Y. Maekawa
  • Organizer: International conference on the Mathematical Fluid Dynamics on the occasion of Professor Yoshihiro Shibata’s 60th birthday
  • Place of Presentation: ホテル日航奈良
  • Invited
• [Presentation] 2次元半空間における渦度方程式の数学解析 (2012)
  • Author(s): 前川泰則
  • Organizer: 2012年度日本数学会年会特別講演
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] 2次元半空間における渦度方程式の数学解析 (2012)
  • Author(s): 前川泰則
  • Organizer: 第61回理論応用力学講演会
  • Place of Presentation: 東京大学生産技術研究所
  • Year and Date: 2012-03-07
• [Presentation] On the inviscid limit problem for viscous incompressible flows in the half plane (2012)
  • Author(s): Maekawa, Y.
  • Organizer: Mathematical theory of turbulence via harmonic analysis and computational fluid dynamics
  • Place of Presentation: Nagoya University
• [Presentation] On the inviscid limit of the Navier-Stokes flows in R^2_+ for initial vorticity located away from the boundary (2012)
  • Author(s): Maekawa, Y.
  • Organizer: Parabolic and Navier-Stokes equations
  • Place of Presentation: Banach center (Poland)
• [Presentation] On fundamental solutions for fractional diffusion equations with divergence drift (2012)
  • Author(s): Maekawa, Y.
  • Organizer: RIMS研究集会異常拡散の数理
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] On zero viscosity limit for the viscous incompressible flows in the half plane (2012)
  • Author(s): Maekawa, Y.
  • 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] Mathematical analysis on some coherent structures of vorticity fields for viscous incompressible flows (2012)
  • Author(s): Maekawa, Y.
  • Organizer: The 5th Japanese-German International Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学
• [Presentation] On vorticity formulation for viscous incompressible flows in the half plane and its application to the inviscid limit problem (2012)
  • Author(s): Maekawa, Y.
  • Organizer: The 4th GCOE international symposium
  • Place of Presentation: Tohoku University
• [Presentation] On zero viscosity limit of viscous incompressible flows in the half plane (2012)
  • Author(s): Y. Maekawa
  • 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
  • Invited
• [Presentation] On zero viscosity limit of viscous incompressible flows in the half plane (2012)
  • Author(s): Y. Maekawa
  • Organizer: Complex Fluid
  • Place of Presentation: ダルムシュタット工科大学
  • Invited
• [Presentation] On fundamental solutions for fractional diffusion equations with divergence free drift (2012)
  • Author(s): 前川泰則
  • Organizer: RIMS研究集会 異常拡散の数理
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] On the inviscid limit of the Navier-Stokes flows in R^2_+ for initial vorticity located away from the boundary (2012)
  • Author(s): Y. Maekawa
  • Organizer: Parabolic and Navier-Stokes equations
  • Place of Presentation: Banach center
  • Invited
• [Presentation] On the inviscid limit problem for viscous incompressible flows in the half plane (2012)
  • Author(s): Y. Maekawa
  • Organizer: Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics
  • Place of Presentation: 名古屋大学
  • Invited
• [Presentation] 2次元半空間Navier-Stokes方程式の零粘性極限問題に対する渦度場からのアプローチ (2012)
  • Author(s): 前川泰則
  • Organizer: 流体乱流の力学と統計-複雑系科学からのアプローチ-
  • Place of Presentation: 支笏湖温泉
• [Presentation] 二次元半空間における渦度方程式の解公式とその応用 (2011)
  • Author(s): 前川泰則
  • Organizer: 北海道大学PDE・Crest合同セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-11-14
• [Presentation] On a priori estimates for axisymmetric solutions to the Navier-Stokes equations (2011)
  • Author(s): Yasunori Maekawa
  • Organizer: ICIAM 2011
  • Place of Presentation: Vancouver (Canada)
  • Year and Date: 2011-07-19
• [Presentation] On fundamental solutions to fractional diffusion equations with a divergence free drift (2011)
  • Author(s): 前川泰則
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Year and Date: 2011-06-25
• [Presentation] On fundamental solutions to fractional heat equations with a divergence free drift term (2011)
  • Author(s): Yasunori Maekawa
  • Organizer: Analysis seminar
  • Place of Presentation: Fourier Institute (Grenoble)
  • Year and Date: 2011-05-16
• [Presentation] On fundamental solutions to fractional diffusion equations with convective terms (2011)
  • Author(s): 前川泰則
  • Organizer: 非線形偏微分方程式-解の性質と形状
  • Place of Presentation: ナジックプラザ東京セミナーホール(東京都)(招待講演)
  • Year and Date: 2011-02-10
• [Presentation] On vorticity concentration at the zero viscosity limit for the Navier-Stokes flows in the half plane (2011)
  • Author(s): Maekawa, Y.
  • Organizer: Third China-Japan Workshop Mathematical Topics from Fluid Mechanics
  • Place of Presentation: Northwest University Xi'an (China)
• [Presentation] On spectral property of the linearization at self-similar solutions for parabolic systems modeling chemotaxis (2011)
  • Author(s): Maekawa, Y.
  • Organizer: The 4th MSJ-SI Nonlinear dynamics in partial differential equation
  • Place of Presentation: Kyushu University
• [Presentation] On estimates for fundamental solutions of diffusion equations related to non-local Dirichlet forms with BMO convections (2011)
  • Author(s): Maekawa, Y.
  • Organizer: 拡散と移流の数理
  • Place of Presentation: 別府
• [Presentation] On vorticity concentration at the zero viscosity limit for the Navier-Stokes flows in the half plane (2011)
  • Author(s): Yasunori Maekawa
  • Organizer: RIMS Camp-style seminar
  • Place of Presentation: Apical Inn Kyoto
• [Presentation] On spectral property of the linearization at self-similar solutions for parabolic systems modeling chemotaxis (2011)
  • Author(s): Yasunori Maekawa
  • Organizer: The 4th MSJ-SI Nonlinear dynamics in partial differential equation
  • Place of Presentation: Kyusyu University
• [Presentation] On vorticity concentration at the zero viscosity limit for the Naiver-Stokes flows in the half plane (2011)
  • Author(s): Yasunori Maekawa
  • Organizer: Third China-Japan Workshop Mathematical Topics from Fluid Mechanics
  • Place of Presentation: Xi'an (China)
• [Presentation] On fundamental solutions to fractional diffusion equations with divergence free drift (2011)
  • Author(s): 前川泰則
  • Organizer: 第3回白浜研究集会
  • Place of Presentation: 南紀白浜温泉
• [Presentation] On fundamental solutions of diffusion equations related to non-local Dirichlet forms with BMO convections (2011)
  • Author(s): Y.Maekawa
  • Organizer: 26th Matsuyama Camp
  • Place of Presentation: 龍谷大学セミナーハウスともいき荘(京都府)(招待講演)
• [Presentation] On estimates for fundamental solutions of diffusion equations related to non-local Dirichlet forms with BMO convections (2011)
  • Author(s): 前川泰則
  • Organizer: 拡散と移流の数理
  • Place of Presentation: 別府(大分県)(招待講演)
• [Presentation] 軸対称Burgers渦に対する安定性解析 (2011)
  • Author(s): 前川泰則
  • Organizer: 第8回城崎新人セミナー
  • Place of Presentation: つたや旅館(兵庫県)(招待講演)
• [Presentation] On evolution equations in the presence of scaling and translation invariances (2010)
  • Author(s): 前川泰則
  • Organizer: 第5回さいたま数理解析セミナー
  • Place of Presentation: 埼玉大学大宮ソニックシティカレッジ(埼玉県)(招待講演)
  • Year and Date: 2010-09-18
• [Presentation] Burgers渦の数学的研究における最近の進展について (2010)
  • Author(s): 前川泰則
  • Organizer: 乱流場と非線形構造-数学と流体力学の融合を目指して-
  • Place of Presentation: 東北大学(宮城県)(招待講演)
  • Year and Date: 2010-04-26
• [Presentation] On semigroup with scaling invariance (2010)
  • Author(s): Maekawa, Y.
  • Organizer: The 7th International Conference on Differential Equations and Dynamical Systems
  • Place of Presentation: University of South Florida (USA)
• [Presentation] On the a priori estimates for axisymmetric solutions to the Navier-Stokes equations (2010)
  • Author(s): Maekawa, Y.
  • 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 (2010)
  • Author(s): Maekawa, Y.
  • Organizer: Fourth Workshop on Nonlinear Partial Differential Equations: Analysis, Computation and Applications
  • Place of Presentation: National Taiwan University (Taiwan)
• [Presentation] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2010)
  • Author(s): Y.Maekawa
  • Organizer: 8th AIMS International Conference
  • Place of Presentation: Dresden(ドイツ)(招待講演)
• [Presentation] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2010)
  • Author(s): Y.Maekawa
  • Organizer: Fourth Workshop on Nonlinear Partial Differential Equations : Analysis, Computation and Applications
  • Place of Presentation: Taipei(台湾)(招待講演)
• [Presentation] On the a priori estimates for axisymmetric solutions to the Navier-Stokes equations (2010)
  • Author(s): Y.Maekawa
  • 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(京都府)(招待講演)
• [Presentation] On semigroup with scaling invariance (2010)
  • Author(s): Y.Maekawa
  • Organizer: The 7th International Conference on Differential Equations and Dynamical Systems
  • Place of Presentation: University of South Florida(米国)(招待講演)