FUJII　Mikihiro

Researcher Information

URL

https://tonpuku.github.io/mikihiro-fujii-homepage/index.html

ORCID ID

•  https://orcid.org/0000-0003-3677-2814

J-Global ID

• 202301019085237080

Research Areas

• Natural sciences / Mathematical analysis / partial differential equations, harmonic analysis

Academic & Professional Experience

• 2024/10 - Today  Nagoya City UniversityGraduate School of Science Division of Mathematical and Material Science講師
• 2023/01 - 2024/09  Kyushu UniversityInstitute of Mathematics for IndustryAssistant Professor
• 2022/10 - 2022/12  Japan Society for the Promotion of Science特別研究員(PD)
• 2020/04 - 2022/09  Japan Society for the Promotion of Science特別研究員(DC1)

Education

• 2020/04 - 2022/09  Kyushu University  Graduate School of Mathematics  Department of Mathematics
• 2018/04 - 2020/03  Kyushu University  Graduate School of Mathematics  Department of Mathematics
• 2014/04 - 2018/03  Kyushu University  School of Sciences  Department of Mathematics

Association Memberships

• 日本数学会   

Published Papers

• Stationary solutions to the critical and super-critical quasi-geostrophic equation in the scaling critical Sobolev space

  Mikihiro Fujii

  Nonlinear Analysis 2026/04
• Global Strong Solutions to the Compressible Navier–Stokes–Coriolis System for Large Data

  Mikihiro Fujii; Keiichi Watanabe

  Archive for Rational Mechanics and Analysis 250 (19) 2026/04 [Refereed]
  
• Incompressible and fast rotation limits for 3D compressible rotating Euler system with general initial data

  Mikihiro Fujii; Yang Li; Pengcheng Mu

  Bulletin of the London Mathematical Society Wiley 58 (3) 0024-6093 2026/02 [Refereed]
  
• Dispersive Phenomena on the Hall-MHD System Around the Constant Equilibrium State in the General Dissipative Coefficients Case

  Mikihiro Fujii; Shunhang Zhang

  Journal of Mathematical Fluid Mechanics Springer Science and Business Media LLC 28 (1) 1422-6928 2026/01
• Linear and nonlinear stability for the 3D stratified Boussinesq equations with the horizontal viscosity and diffusivity

  Mikihiro Fujii; Yang Li

  SIAM Journal on Mathematical Analysis 2026/01 [Refereed]
  
• Time-periodic solutions to the Navier–Stokes equations on the whole space including the two-dimensional case

  Mikihiro Fujii

  Annales de l'Institut Henri Poincaré C, Analyse non linéaire European Mathematical Society - EMS - Publishing House GmbH 0294-1449 2025/12 [Refereed]
  
• Sharp well-posedness and ill-posedness of the stationary quasi-geostrophic equation

  Mikihiro Fujii; Tsukasa Iwabuchi

  Mathematische Annalen 2025/08 [Refereed]
  
• Stationary Navier–Stokes equations on the half spaces in the scaling critical framework

  Mikihiro Fujii

  Journal of Differential Equations 2025/08 [Refereed]
  
• Compressible Navier–Stokes–Coriolis system in critical Besov spaces

  Mikihiro Fujii; Keiichi Watanabe

  Journal of Differential Equations Elsevier BV 428 747 - 795 0022-0396 2025/05 [Refereed]
  
• Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework

  Mikihiro Fujii; Yang Li

  Calculus of Variations and Partial Differential Equations 2025/01 [Refereed]
  
• Large Time Behavior for Solutions to the Anisotropic Navier–Stokes Equations in a 3D Half-space

  Mikihiro Fujii; Yang Li

  International Mathematics Research Notices Oxford University Press (OUP) 1073-7928 2024/12 [Refereed]
  
• Well‐posedness of the two‐dimensional stationary Navier–Stokes equations around a uniform flow

  Mikihiro Fujii; Hiroyuki Tsurumi

  Mathematische Nachrichten 2024/12 [Refereed]
  
• Global solutions for the incompressible Hall-magnetohydrodynamics system around constant equilibrium states

  Mikihiro Fujii; Ryosuke Nakasato

  Journal of Mathematical Analysis and Applications 2024/08 [Refereed]
  
• Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane

  Mikihiro Fujii

  Annals of PDE Springer Science and Business Media LLC 10 (1) 2524-5317 2024/05 [Refereed]
  
• Global solutions to the rotating Navier–Stokes equations with large data in the critical Fourier–Besov spaces

  Mikihiro Fujii

  Mathematische Nachrichten 2024/05 [Refereed]
  
• Low Mach number limit of the global solution to the compressible Navier–Stokes system for large data in the critical Besov space

  Mikihiro Fujii

  Mathematische Annalen 2024/04 [Refereed]
  
• Global well-posedness of the incompressible Hall-MHD system in critical spaces

  Mikihiro Fujii

  Journal of Evolution Equations 2024/03 [Refereed]
  
• Large time behavior of solutions to the 3D anisotropic Navier–Stokes equation

  Mikihiro Fujii

  Nonlinear Analysis: Real World Applications Elsevier BV 71 103821 - 103821 1468-1218 2023/06 [Refereed]
  
• Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing

  Mikihiro FUJII

  Journal of the Mathematical Society of Japan Mathematical Society of Japan (Project Euclid) 75 (1) 0025-5645 2023/01 [Refereed]
  
• Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation

  Mikihiro Fujii

  Journal of Evolution Equations Springer Science and Business Media LLC 22 (1) 1424-3199 2022/03 [Refereed]
  
• Isolated singularities in the heat equation behaving like fractional Brownian motions

  Mikihiro Fujii; Izumi Okada; Eiji Yanagida

  Journal of Mathematical Analysis and Applications Elsevier BV 504 (1) 125322 - 125322 0022-247X 2021/12 [Refereed]
  
• Long Time Existence and Asymptotic Behavior of Solutions for the 2D Quasi-geostrophic Equation with Large Dispersive Forcing

  Mikihiro Fujii

  Journal of Mathematical Fluid Mechanics Springer Science and Business Media LLC 23 (1) 1422-6928 2020/11 [Refereed]
  

Awards & Honors

• 2026/09 一般社団法人「日本数学会」 日本数学会賞建部賢弘賞特別賞
   Well-posedness and long time behavior of solutions for the fluid mechanics via the method of harmonic analysis
• 2020 日本数学会九州支部会 第 9 回九州若手数学賞
   Asymptotic behavior in time of solutions for the quasi-geostrophic equation with dispersion
• 2019 日本数学会九州支部会 第 5 回九州若手数学者発表賞受賞者
   Long time solutions of the quasi-geostrophic equation with strong dispersive forcing

Research Grants & Projects

• 2次元粘性流体方程式の定常問題に対する非可解性の数学解析

  日本学術振興会：科学研究費助成事業

  Date (from‐to) : 2025/04 -2029/03 

  Author : 藤井 幹大
• Mathematical analysis for the compressible viscous rotating flow

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2023/08 -2025/03 

  Author : 藤井 幹大
• Analysis of dispersive effects for partial differential equations appeared in the geophysical fluid dynamics

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

  Date (from‐to) : 2020/04 -2023/03 

  Author : 藤井 幹大

   

  令和3年度は，異方的粘性項を持つNavier-Stokes方程式，Hall-MHD方程式および圧縮性回転Navier-Stokes方程式について研究した． 異方的粘性項を持つNavier-Stokes方程式は3次元非圧縮性Navier-Stokes方程式において，その粘性項のLaplacianを水平方向の成分のみからなる2次元Laplacianとしたものである．この方程式の適切性の研究は20年ほど前に創始され，多くの研究結果が存在する．一方で時間大域解の時刻無限大での漸近挙動に関する研究はあまりみられなかった．本研究では，粘性項の異方性が解の長時間挙動に与える影響を定性的に明らかにすることを目標とし研究を行った．そして，解の水平成分は2次元の熱核と同一の時間減衰率を示し，解の鉛直成分は3次元の熱核と同じ時間減衰率持つという結果を得た．特に解の時刻無限大における漸近展開を行うと，その水平成分の主要部に非線形性が現れることが明らかとなった． 次に，Hall-MHD方程式を定磁場周りで考察した．空間遠方の定磁場の呈する分散性を制御するためにFourier-Besov空間を用いて尺度不変な枠組みで時間大域的適切性を証明した．本研究では低周波部分の評価の改善や線型解の具体的な解公式の導出に成功したことで，先行研究で知られていた結果を適切性が保証される関数空間のクラスの観点で大幅に改善することができた．本研究は中里亮介氏（早稲田大学）との共同研究に基づく． さらに，圧縮性回転Navier-Stokes方程式を考察した．特に回転と音波による分散性について臨界Besov空間における解析を行い，任意の有限時刻と臨界Besov空間に属する任意の初期値に対して，回転速度を十分大きくかつマッハ数を十分小さくとると，与えられた有限時刻までの解が一意的に存在することを証明した．本研究は渡邊圭市氏(早稲田大学)との共同研究である．

Other link

researchmap

https://researchmap.jp/mikihirofujii