Analysis of singularity of solutions to the Navier-Stokes equations

• Project/Area Number: 21740106
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kanagawa University
• Principal Investigator: SUZUKI Tomoyuki Kanagawa University, 工学部, 助手 (80452423)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 偏微分方程式 / 関数方程式論

Research Abstract

We prove regularity of weak solutions to the Navier-Stokes equations under the conditions on the pressure. In particular, we exelude the possibility of blow-up in the case that the pressure is small enough in scaling invariant spaces based on Lorentz spaces. This result can be applied to MHD equations if the magnetic field in addition to the pressure belongs to the scaling invariant spaces based on the Lorentz spaces with small norms.

Research Products

• [Journal Article] Regularity criteria of weak solutions in terms of the pressure to the Navier-Stokes equations in weak spaces (2011)
  • Author(s): Tomoyuki Suzuki
  • Journal Title: AIMS Proceedings Volume: (掲載確定)
  • Peer Reviewed
• [Journal Article] Regularity criteria in weak spaces in terms of the pressure to the MHD equations
  • Author(s): T.Suzuki
  • Journal Title: AIMS proceeding 掲載確定
• [Presentation] Navier-Stokes方程式のエネルギー等式について (2010)
  • Author(s): 鈴木友之
  • Organizer: 2010年度日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-25
• [Presentation] Navier-Stokes方程式のエネルギー等式について (2010)
  • Author(s): 鈴木友之
  • Organizer: 日本数学会2011年度秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-25
• [Presentation] On regularity of weak solutions to the Navier-Stokes equations in Lorentz spaces (2010)
  • Author(s): 鈴木友之
  • Organizer: 若手による流体力学基礎方程式研究集会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-07-06
• [Presentation] Regularity criterion via pressure in Lorentz spaces to the MHD equations (2010)
  • Author(s): 鈴木友之
  • Organizer: AIMS conference
  • Place of Presentation: Dresden University of Technology, Germany
  • Year and Date: 2010-05-25
• [Presentation] Regularity criterion for weak solutions in weak spaces in terms of the pressure to the MHD equations (2010)
  • Author(s): Tomoyuki Suzuki
  • Organizer: 8th AIMS conference
  • Place of Presentation: ドイツ ドレスデン ドレスデン工科大学(招待講演)
  • Year and Date: 2010-05-25
• [Presentation] Regularity criterion of weak solutions via pressure in Lorentz spaces to the Navier-Stokes equations (2010)
  • Author(s): 鈴木友之
  • Organizer: Workshop on PDE
  • Place of Presentation: University of Paderborn, Germany
  • Year and Date: 2010-03-03
• [Presentation] Regularity criterion of weak solutions via pressure in Lorentz space to the Navier-Stokes equations (2010)
  • Author(s): Tomoyuki Suzulri
  • Organizer: Workshop on partial differential equations
  • Place of Presentation: ドイツパダーボルン大学
  • Year and Date: 2010-03-03
• [Presentation] Regularity criterion of weak solutions in terms of the pressure to the Navier-Stokes equations in Lorentz spaces (2010)
  • Author(s): 鈴木友之
  • Organizer: Seminar on partial differential equations
  • Place of Presentation: 韓国西江大学
  • Year and Date: 2010-01-29
• [Presentation] Survey on regularity criteria to the Navier-Stokes equations in Lorentz space (2010)
  • Author(s): 鈴木友之
  • Place of Presentation: Sogang University, 韓国
  • Year and Date: 2010-01-28
• [Presentation] On regularity of weak solutions to the Navier-Stokes equations in Lorentz snace (2010)
  • Author(s): 鈴木友之
  • 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: 2010-01-06
• [Presentation] 圧力の条件の下でのNavier-Stokes方程式の弱解の正則性について (2009)
  • Author(s): 鈴木友之
  • Organizer: 2009年度日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] 圧力に対する条件の下でのNavier-Stokea方程式の弱解の正則性定理について (2009)
  • Author(s): 鈴木友之
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Remarks] ホームページ等
• [Remarks]
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinId=ymbggsyeggg
• [Remarks]
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinld=ymbggsyeggg