• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2018 Fiscal Year Annual Research Report

Invention and explorer for undiscovered structure and principle in the mathematical analysis for the relation between fluid dynamics and combustion.

Research Project

Project/Area Number 17H06199
Allocation TypeSingle-year Grants
Research InstitutionTohoku University

Principal Investigator

小川 卓克  東北大学, 理学研究科, 教授 (20224107)

Co-Investigator(Kenkyū-buntansha) 岩渕 司  東北大学, 理学研究科, 准教授 (40634697)
丸田 薫  東北大学, 流体科学研究所, 教授 (50260451)
服部 裕司  東北大学, 流体科学研究所, 教授 (70261469)
石毛 和弘  東京大学, 大学院数理科学研究科, 教授 (90272020)
Project Period (FY) 2017-06-30 – 2023-03-31
Keywords非圧縮性Navier-Stokes 方程式 / 臨界適切性 / 非線型熱方程式 / 有界平均振動のクラス / 動的境界条件 / 非圧縮性Navier-Stokes 方程式 / 可解性 / 最大正則性
Outline of Annual Research Achievements

研究代表者の小川は燃焼系のダイナミクスに大きな与える, 圧縮性・非圧縮性Navier-Stokes方程式に対する臨界適切性を研究した. とりわけ非圧縮性粘性流体方程式の時間大域可解性を考察するうえでスケール臨界におけるもっとも広い空間である, 有界平均振動(BMO)のクラスに対して線形の熱方程式及びStokes方程式の解の最大正則性を議論し, 清水扇丈氏(京大人環)と共同で有界平均振動のクラスにおける最大正則性とその最良初期トレース評価を確立した. この結果は非圧縮性粘性流体の初期値問題の可解性をFujita-Katoの原理に基づいて研究するうえで今日知られているもっとも広い空間であり, またKoch-Tataruに寄る可解性の結果に相当する構造を準線形問題に拡張できる可能性をもつ一般的な評価である. 特に有界平均振動のクラスは回帰的ではないので, 最大正則性の一般論に依る構成の必要条件である無条件円チーンゲール差性が破綻することに注意する. 今回の研究で, こうした困難が回避されBMOにおける様々な粘性流体方程式(たとえばHall効果をもつ磁気粘性流体など)の可解性が議論できるようになった.
また分担者の石毛は燃焼系に直接関わる, 非線型熱方程式の研究を進め, 非線形分数冪拡散方程式が可解であるために許容できる初期関数の特異性の特徴付けを行い、可解であるための最善な十分条件を得た。また、非線形境界条件や動的境界条件化における放物型方程式の可解性や定性的性質についても研究を行った。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

非圧縮性粘性流体に対する様々な臨界可解性研究と燃焼過程に重要な非線型熱方程式や反応拡散方程式の適切性に対する臨界適切性といった重要な問題に大きな進展が見られる. こうした問題の結果が実学でどのように観察されるかについて今後の研究の糸口が開きつつあるように見られる.

Strategy for Future Research Activity

BMOでの最大正則性の確立により, 準線形の問題, たとえばHall効果をもつ非圧縮性Navier-Stokes 方程式の可解性が議論できるようになった. このため, Hall効果や燃焼に関わる反応拡散系との連立型における, 有界平均振動のクラスについて議論を進める. また燃焼問題特異火炎球の解析に必要な初期値境界値問題に対するFujia-Katoの原理が展開可能かどうかについてもっとも単純な初期値境界値問題に対する, 初期値境界値問題の最大正則性を臨界空間で考察するなどを検討する.

  • Research Products

    (21 results)

All 2019 2018 Other

All Journal Article (14 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 14 results) Presentation (5 results) (of which Int'l Joint Research: 5 results,  Invited: 5 results) Remarks (1 results) Funded Workshop (1 results)

  • [Journal Article] Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations2019

    • Author(s)
      Ioku Norisuke、Ogawa Takayoshi
    • Journal Title

      Journal of Differential Equations

      Volume: 266 Pages: 2274~2293

    • DOI

      doi:10.1016/j.jde.2018.08.030

    • Peer Reviewed
  • [Journal Article] Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle2018

    • Author(s)
      Ogawa T., Seraku K.,
    • Journal Title

      Communications on Pure & Applied Analysis

      Volume: 17 Pages: 1651~1669

    • DOI

      doi:10.3934/cpaa.2018079

    • Peer Reviewed
  • [Journal Article] Remark on the uniqueness of a weak mild solution of the Boltzmann equation in a critical Besov space2018

    • Author(s)
      T. Ogawa, S. Shimizu,
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 67 Pages: 83-105

    • Peer Reviewed
  • [Journal Article] Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle2018

    • Author(s)
      Kubo Hideo、Ogawa Takayoshi、Suguro Takeshi
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 147 Pages: 1511~1518

    • DOI

      doi.org/10.1090/proc/14350

    • Peer Reviewed
  • [Journal Article] Large time behavior of solutions of the heat equation with inverse square potential,2018

    • Author(s)
      K. Ishige and A. Mukai,
    • Journal Title

      Discrete Contin. Dyn. Syst.

      Volume: 38 Pages: 4041-4069

    • Peer Reviewed
  • [Journal Article] Existence of solutions for a fractional semilinear parabolic equation with singular initial data,2018

    • Author(s)
      K. Hisa and K. Ishige,
    • Journal Title

      Nonlinear Anal.

      Volume: 175 Pages: 108-132

    • Peer Reviewed
  • [Journal Article] The semigroup generated by the Dirichlet Laplacian of fractional order2018

    • Author(s)
      T. Iwabuchi
    • Journal Title

      Anal. PDE

      Volume: 11 Pages: 683_703

    • DOI

      DOI: 10.2140/apde.2018.11.683

    • Peer Reviewed
  • [Journal Article] Derivatives on Function Spaces Generated By the Dirichlet Laplacian and the Neumann Laplacian in One Dimension2018

    • Author(s)
      T. Iwabuchi
    • Journal Title

      Commun. Math. Anal.

      Volume: 21 Pages: 1_8

    • Peer Reviewed
  • [Journal Article] Boundedness of spectral multipliers for Schr_dinger operators on open sets2018

    • Author(s)
      T. Iwabuchi, T. Matsuyama, K. Taniguchi
    • Journal Title

      Rev. Mat. Iberoam.

      Volume: 34 Pages: 1277-1322

    • DOI

      DOI: 10.4171/RMI/1024

    • Peer Reviewed
  • [Journal Article] Generalized Contour Dynamics: A Review2018

    • Author(s)
      Stefan G. Llewellyn Smith, Ching Chang, Tianyi Chu, Mark Blyth, Yuji Hattori, and Hayder Salman
    • Journal Title

      Regul. Chaotic Dyn.

      Volume: 23 Pages: 507-518

    • DOI

      doi:10.1134/S1560354718050027

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Strato-hyperbolic instability: a new mechanism of instability in stably stratified vortices2018

    • Author(s)
      Shota Suzuki, Makoto Hirota and Yuji Hattori
    • Journal Title

      J. Fluid Mech.

      Volume: 854 Pages: 293-323

    • DOI

      doi:10.1017/jfm.2018.641

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Experimental and numerical study of premixed flame penetration and propagation in multichannel system2018

    • Author(s)
      Roman Fursenko, Evgeniy Sereshchenko, Georgii Uriupin, Egor Odintsov, Takuya Tezuka, Sergey Minaev, Kaoru Maruta
    • Journal Title

      Combustion Science and Technology

      Volume: 190 Issue 6 Pages: 1023-1040

    • DOI

      doi:10.1080/00102202.2018.1424143

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Broken C-shaped extinction curve and near-limit flame behaviors of low Lewis number counterflow flames under microgravity2018

    • Author(s)
      Tomoya Okuno, Takaki Akiba, Hisashi Nakamura, Roman Fursenko, Sergey Minaev, Takuya Tezuka, Susumu Hasegawa, Masao Kikuchi, Kaoru Maruta
    • Journal Title

      Combustion and Flame

      Volume: 194 Pages: 343-351

    • DOI

      doi.org/10.1016/j.combustflame.2018.05.014

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Evaluation of the reactivity of ultra-lean PRF/air mixtures by weak flames in a micro flow reactor with a controlled temperature profile2018

    • Author(s)
      Philipp Grajetzki, Hisashi Nakamura, Takuya Tezuka, Susumu Hasegawa and Kaoru Maruta
    • Journal Title

      Combustion Science and Technology

      Volume: 190 Issue 11 Pages: 1950-1970

    • DOI

      doi.org/10.1080/00102202.2018.1477772

    • Peer Reviewed
  • [Presentation] Maximal regularity for the Cauchy problem of the heat equation in the class of bounded mean oscillation2019

    • Author(s)
      T. Ogawa
    • Organizer
      Zhuhai PDE workshop
    • Int'l Joint Research / Invited
  • [Presentation] Maximal regularity for the Cauchy problem for the Stokes system in BMO2019

    • Author(s)
      T. Ogawa
    • Organizer
      Maximal Regularity and Nonlinear PDE
    • Int'l Joint Research / Invited
  • [Presentation] Illposedness for the compressbile Navier-Stokes system in the critical Besov spaces2018

    • Author(s)
      T. Ogawa
    • Organizer
      2018 PDE workshop in Hangzhou
    • Int'l Joint Research / Invited
  • [Presentation] Ill-posedness issue for the compressible Navier-Stokes equation under the barotropic assumption in the critical Besov space2018

    • Author(s)
      T. Ogawa
    • Organizer
      Mathematical Fluid Mechnaics
    • Int'l Joint Research / Invited
  • [Presentation] Well-posedness of the initial value problem for incompressible Navier-Stokes equations under the Lagrangian coordinate2018

    • Author(s)
      T. Ogawa
    • Organizer
      Mathematical Fluid Mechanics and Related Topics
    • Int'l Joint Research / Invited
  • [Remarks] 東北大学数理科学連携研究センター パターンダイナミクス解析研究部門

    • URL

      http://www.racmas.tohoku.ac.jp/category_02.html

  • [Funded Workshop] Critical Exponent and Partial Differential Equations 20192019

URL: 

Published: 2021-01-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi