A regularity criterion for the harmonic map flows and asymptotic analysis for singularity

• Project/Area Number: 21540222
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kumamoto University
• Principal Investigator: MISAWA Masashi 熊本大学, 大学院・自然科学研究科, 教授 (40242672)
• Co-Investigator(Renkei-kenkyūsha): TONEGAWA Yoshihiro 北海道大学, 大学院・理学研究科, 教授 (80296748) ; YAMAURA Yoshihiko 日本大学, 文理学部, 教授 (90255597)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 調和写像 / 調和写像流 / 変分問題 / 弱解 / 大域存在 / 正則性 / 特異性 / p調和写像 / p調和写像流 / 正則性評価 / 国際共同研究 / p調和作用素 / 国際研究者交流 / 国際情報交換 / 漸近解析 / 幾何学的変分問題

Research Abstract

I consider the evolution of the harmonic maps, called the harmonic map flows. In particular, I study the global existence and regularity of weak solutions of the harmonic map flows. I improve the regularity criterion for weak solutions and show the global existence of the dissipative wave equations, with applications to the wave maps.

Research Products

• [Journal Article] A global existence result for the heat flow of higher dimensional H-systems (2011)
  • Author(s): C. Leone, M. Misawa, A. Verde
  • Journal Title: J. Math. Pures Appl. Volume: 97巻 Pages: 282-294
  • Peer Reviewed
• [Journal Article] Decay property for the linear wave equations in two dimens ional exterior domains (2011)
  • Author(s): T. Kobayashi, M, Misawa, S. Okamura
  • Journal Title: Differential and Integral Equations Volume: 24巻 Pages: 941-964
  • Peer Reviewed
• [Journal Article] Decay property for the linear wave equations in two dimensional exterior domains (2011)
  • Author(s): T.Kobayashi, M.Misawa, S.Okamura
  • Journal Title: Differential and Integral Equations Volume: 24 Pages: 941-964
  • Peer Reviewed
• [Journal Article] A global existence result for the heat flow of higher dimensional H-systems (2011)
  • Author(s): C.Leone, M.Misawa, A, Verde
  • Journal Title: J.Math.Pures Appl. Volume: 97 Issue: 3 Pages: 282-294
  • DOI: 10.1016/j.matpur.2011.11.001
  • Peer Reviewed
• [Journal Article] Decay property for the linear wave equations in two dimensional exterior domains (2010)
  • Author(s): T.Kobayashi, M.Misawa, S.Okamura
  • Journal Title: Differential and Integral Equations Volume: 2010(掲載決定)
  • Peer Reviewed
• [Presentation] A Holder estimate for evolutional p-Laplacian systems and its application (2012)
  • Author(s): Masashi Misawa
  • Organizer: 第4回名古屋微分方程式研究集会
  • Place of Presentation: 名古屋大学(nagoya)(杉本充教授による招待講演)
  • Year and Date: 2012-03-06
• [Presentation] A Holder estimate for evolutional p-Laplacian systems and its application (2012)
  • Author(s): 三沢正史(Masashi Misawa)
  • Organizer: 第4回名古屋微分方程式研究集会(The 4^<th> Nagoya Workshop on Differential Equations)
  • Place of Presentation: 名古屋大学理1号館509号室(招待講演)
  • Year and Date: 2012-03-06
• [Presentation] p調和型非線形放物型方程式系に対するヘルダー評価とその幾何学的偏微分方程式への応用 (2012)
  • Author(s): 三沢正史
  • Organizer: 解析セミナー
  • Place of Presentation: 愛媛大学(内藤雄基教授による招待講演)
  • Year and Date: 2012-01-21
• [Presentation] A Holder regularity for nonlinear parabolic systems of p-Laplacian type (2011)
  • Author(s): Masashi Misawa
  • Organizer: Department of Mathematics
  • Place of Presentation: Aalto University(Helsinki, Finland)(Juha Kinnunen教授による招待講演)
  • Year and Date: 2011-12-08
• [Presentation] ある退化放物型方程式系に対するヘルダー評価について (2010)
  • Author(s): 三沢正史
  • Organizer: 大阪大学微分方程式セミナー
  • Place of Presentation: 大阪大学大学院理学研究科(大阪)(鈴木貴教授による招待講演)
  • Year and Date: 2010-12-10
• [Presentation] ある退化放物型方程式に対するヘルダー評価について (2010)
  • Author(s): 三沢正史
  • Organizer: 大阪大学微分方程式セミナー
  • Place of Presentation: 大阪大学大学院理学研究科
  • Year and Date: 2010-12-10
• [Presentation] 時間発展p調和方程式系に対する正則性評価について (2010)
  • Author(s): 三沢正史
  • Place of Presentation: 九州工業大学数学教室
  • Year and Date: 2010-11-13
• [Presentation] A refeined Holder estimate for the evolutional p-Laplacian systems (2010)
  • Author(s): Masashi Misawa
  • Organizer: 成均館大学数学科
  • Place of Presentation: 韓国,水原(Kyungkeun Kang教授の招待講演)
  • Year and Date: 2010-10-16
• [Presentation] p調和型方程式系に対するあるヘルダー評価について (2010)
  • Author(s): 三沢正史
  • Organizer: 奈良における偏微分方程式研究集会
  • Place of Presentation: 奈良女子大学数学科(柳沢卓准教授による招待講演)
  • Year and Date: 2010-06-26
• [Presentation] Regularity by small BMO for the harmonic map flo ws (2009)
  • Author(s): Masashi Misawa
  • Organizer: Department of Napoli University
  • Place of Presentation: Napoli, Italy(Nicola Fusco教授による招待講演)
  • Year and Date: 2009-09-10
• [Presentation] Regularity by small BMO for the harmonic map flows (2009)
  • Author(s): Masashi Misawa
  • Organizer: Napoli University, Analysis Seminar(Editor : Nicola Fusco)
  • Place of Presentation: Department of Mathematics, Napoli University, Italy
  • Year and Date: 2009-09-10
• [Presentation] 調和写像流に対する正則性条件の改良について (2009)
  • Author(s): 三沢正史
  • Organizer: 埼玉大学数学科談話会
  • Year and Date: 2009-06-24
• [Remarks]
  • URL: http://www.sci.kumamoto-u.ac.jp