Study on stationary solution to non-linear PDE in Fluid Dynamics

• Project/Area Number: 18740081
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: University of Tsukuba (2008); Waseda University (2006-2007)
• Principal Investigator: KUBO Takayuki University of Tsukuba, 大学院・数理物質科学研究科, 助教 (90424811)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,670,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,300,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 関数方程式 / 流体力学 / Navier-Stokes方程式 / 安定性 / 非線形現象

Research Abstract

本研究において,流体力学の基礎方程式であるナヴィエ・ストークス方程式の半空間とその摂動で与えられる領域における,時間局所解と小さい初期値に対する時間大域解の一意存在性を証明した.また,3次元以上の半空間において無限遠で全空間や外部領域よりも早く減衰する定常解の存在とその安定性を証明した.さらに,半空間の摂動として与えられる領域において,すでに得られていた定常解の小さい初期摂動に関する漸近安定性を証明した.

Research Products

• [Journal Article] The Stokes and Navier-Stokes equations in an aperture domain (2008)
  • Author(s): T. Kubo
  • Journal Title: 研究集会"流体と気体の数学解析",数理解析研究所講究録 1592 Pages: 53-68
  • NAID: 10019540096
• [Journal Article] The Stokes and Navier-Stokes equations in an aperture domain (2008)
  • Author(s): 久保隆徹
  • Journal Title: 数理解析研究所講究録 1592 Pages: 53-68
  • NAID: 10019540096
• [Journal Article] The Stokes and Navier-Stokes equations in an aperture domain (2007)
  • Author(s): T. Kubo
  • Journal Title: J. Math. Soc. Japan Vol.59, No.3 Pages: 837-859
  • NAID: 10019540096
  • Peer Reviewed
• [Journal Article] On the Stokes and Navier-Stokes equations in a perturbef half-space and an aperture domain (2007)
  • Author(s): T.Kubo
  • Journal Title: Asymptotic Analysis and Singularities, Hyperbolic and dispersive PDEs and fluid mechanics, 47-1, Advanced Studies in Pure Mathematics, T. Kohno et al. ed. Tokyo Shoseki Printing Co. Pages: 169-187
  • Peer Reviewed
• [Journal Article] The Stokes and Navier-Stokes equations in an apreture domain (2007)
  • Author(s): Takayuki Kubo
  • Journal Title: Journal of the Mathematical Society of Japan 59 Pages: 837-859
  • Peer Reviewed
• [Journal Article] L^p-L^q estimate of the Stokes semigroup and its application to Navier-Stokes equation in a perturbed half-space (2006)
  • Author(s): T.Kubo and Y.Shibata
  • Journal Title: Hyperbolic Problems, Theory, Numerics and Applications, II, Asakura et al. ed. Yokohama Publishers Pages: 125-132
  • Peer Reviewed
• [Presentation] Navier-Stokes flow in an aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: 研究集会「微分方程式の総合的研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-12-20
• [Presentation] On Stokes and Navier-Stokes flow in an aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: 研究集会「曲線と曲面の非線形解析」
  • Place of Presentation: 埼玉大学
  • Year and Date: 2008-12-16
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: First China-Japan workshop on Mathematical Topics from Fluid Mechanics
  • Place of Presentation: 北京大学(中国)
  • Year and Date: 2008-11-12
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: First China-Japan workshop on Mathematical Top ics from Fluid Mechanics
  • Place of Presentation: 北京大学
  • Year and Date: 2008-11-12
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: ダルムシュタット工科大学(ドイツ)
  • Year and Date: 2008-09-09
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: ダイムシュタット工科大学(ドイツ)
  • Year and Date: 2008-09-07
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: The Banach Center Conference "Parabolic and Navier-Stokes Equations 2008"
  • Place of Presentation: Bedlevo(ポーランド)
  • Year and Date: 2008-09-02
• [Presentation] Stability of stationary Navier-Stokes flow in a two-dimensional aperture domain (2008)
  • Author(s): 久保隆徹
  • Organizer: Parabolic and Navier-Stokes Equations 2008
  • Place of Presentation: バナッハセンター(ポーランド)
  • Year and Date: 2008-09-02
• [Presentation] 2次元aperture domainでの非圧縮粘性流の安定性 (2008)
  • Author(s): 久保隆徹
  • Organizer: 日本数学会年会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-25
• [Presentation] aperture domain における非圧縮粘性流について (2008)
  • Author(s): 久保隆徹
  • Organizer: 東工大・早稲田ミニシンポジウム
  • Place of Presentation: 早稲田大学
  • Year and Date: 2008-01-12
• [Presentation] aperture domainにおける非圧縮粘性流について (2008)
  • Author(s): 久保隆徹
  • 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
  • Year and Date: 2008-01-05
• [Presentation] aperture domainにおける非圧縮粘性流について (2008)
  • Author(s): 久保隆徹
  • Organizer: 東工大・早稲田ミニシンポジウム
  • Place of Presentation: 早稲田大学
• [Presentation] apeture domainでの非圧縮粘性流について (2008)
  • Author(s): 久保隆徹
  • Organizer: 筑波大学解析セミナー
  • Place of Presentation: 筑波大学
• [Presentation] Navier-Stokes flow in an aperture domain (2007)
  • Author(s): 久保隆徹
  • Organizer: 第9回流体と気体の数学解析
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-07-12
• [Presentation] Navier-Stokes flow in an apretue domain (2007)
  • Author(s): 久保隆徹
  • Organizer: 応用数学に関する愛媛ワークショップ
  • Place of Presentation: 愛媛大学
  • Year and Date: 2007-03-17
• [Presentation] Navier-Stokes flow in an aperture domain (2007)
  • Author(s): 久保隆徹
  • Organizer: 第9回流体と気体の数学解析
  • Place of Presentation: 京都大学
• [Presentation] The Navier-Stokes flow in the aperture domain (2006)
  • Author(s): 久保隆徹
  • Organizer: 第4回浜松偏微分方程式研究集会
  • Place of Presentation: 静岡大学
  • Year and Date: 2006-12-10
• [Presentation] The Stokes and Navier-Stokes equations in the aperture domain (2006)
  • Author(s): 久保隆徹
  • Organizer: The Banach Center Conference "Parabolic and Navier-Stokes Equations"
  • Place of Presentation: Bedlevo(ポーランド)
  • Year and Date: 2006-09-14
• [Presentation] The Stokes and Navier-Stokes equations in the aperture domain (2006)
  • Author(s): 久保隆徹
  • Organizer: Evolution Equation 2006
  • Place of Presentation: (Mons(Belgium) and Valenciennes(France)
  • Year and Date: 2006-08-31
• [Presentation] On the Navier-Stokes flows with a nontrivial flux conditon in an aperture domain (2006)
  • Author(s): 久保隆徹
  • Organizer: 第28回若手発展方程式セミナー
  • Place of Presentation: 六甲山
  • Year and Date: 2006-08-09