Mikihiro Fujii

Refined decay estimates for global solutions to the rotating MHD equations

Mikihiro Fujii, Yang Li

In this paper, we consider the Cauchy problem for the incompressible magnetohydrodynamic equations with the Coriolis force in the three-dimensional whole space. For large initial d…

Non-unique $L^{2}$ solutions to the stationary Navier--Stokes equations on the whole plane

Mikihiro Fujii

We prove that, for a suitable small external force in $H ˙^{- 2} (R^{2})$ , the stationary Navier--Stokes equations on $R^{2}$ admit multiple solutions in $L^2(\mathbb…

Sharp decay estimates for global solutions to the incompressible rotating Navier--Stokes equations

Mikihiro Fujii, Yang Li, Jiang Xu

In this paper, we consider the three-dimensional incompressible rotating Navier--Stokes equations and establish the sharp $L^{p}$ decay estimates of global solutions. We reveal that…

Global solutions to the Navier--Stokes equations with large vertical velocities in $B ˙_{\infty, σ}^{- 1} (R^{3})$

Mikihiro Fujii

In this paper, we consider the Cauchy problem for the $3$ D incompressible Navier--Stokes equations and prove the existence of unique global solutions in the framework that the hori…

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces

Mikihiro Fujii

It is known that uniqueness of mild solutions to the incompressible Navier-Stokes equations holds in the critical class $C ([0, T); L^{n} (R^{n}))$ for $n ⩾ 3$ . In this pa…

Analyticity in space and time for global solutions to the anisotropic Navier--Stokes equations in the critical $L^{p} (R^{3})$ framework

Mikihiro Fujii, Yang Li

In the present paper, we consider the real analyticity of the global solutions to the $3$ D incompressible anisotropic Navier--Stokes equations. We show that if only the horizontal…

Global strong solutions to the $3$ D rotating compressible Navier--Stokes--Korteweg system for large data in the critical $L^{p}$ framework

Mikihiro Fujii, Shunhang Zhang

Let us consider the $3$ D compressible Navier--Stokes--Korteweg system in the rotational framework. Although there is a wealth of literature on the weak solutions to this system, th…

Asymptotic instability for the forced Navier--Stokes equations in critical Besov spaces

Mikihiro Fujii, Hiroyuki Tsurumi

The asymptotic stability is one of the classical problems in the field of mathematical analysis of fluid mechanics. In $R^{n}$ with $n \geq 3$ , it is easily proved by the st…

Decay rates of three dimensional stationary Navier--Stokes flows at the spatial infinity

Mikihiro Fujii, Hiroyuki Tsurumi, Xin Zhang

In this paper, we establish the well-posedness results of the three dimensional stationary Navier--Stokes equations (SNS) in some critical hybrid type Besov spaces with respect to…

Incompressible and fast rotation limits for 3D compressible rotating Euler system with general initial data

Mikihiro Fujii, Yang Li, Pengcheng Mu

This paper is concerned with the low Mach and Rossby number limits of $3$ D compressible rotating Euler equations with ill-prepared initial data in the whole space. More precisely,…

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

Mikihiro Fujii

We consider the stationary problem for the quasi-geostrophic equation with the critical and super-critical dissipation and prove the unique existence of small solutions for given s…

Sharp well-posedness and ill-posedness of the stationary quasi-geostrophic equation

Mikihiro Fujii, Tsukasa Iwabuchi

We consider the stationary problem for the quasi-geostrophic equation on the whole plane and investigate its well-posedness and ill-posedness. In[Fujii, Ann. PDE 10, 10 (2024)], it…

Global strong solutions to the compressible Navier--Stokes--Coriolis system for large data

Mikihiro Fujii, Keiichi Watanabe

We consider the compressible Navier--Stokes system with the Coriolis force on the $3$ D whole space. In this model, the Coriolis force causes the linearized solution to behave like…

Compressible Navier--Stokes--Coriolis system in critical Besov spaces

Mikihiro Fujii, Keiichi Watanabe

We consider the three-dimensional compressible Navier--Stokes system with the Coriolis force and prove the long-time existence of a unique strong solution. More precisely, we show…

Linear and nonlinear stability for the $3$ D stratified Boussinesq equations with the horizontal viscosity and diffusivity

Mikihiro Fujii, Yang Li

In this manuscript, we consider the $3$ D Boussinesq equations for stably stratified fluids with the horizontal viscosity and thermal diffusivity and investigate the large time beha…

Low Mach number limit for the global large solutions to the $2$ D Navier--Stokes--Korteweg system in the critical $L^{p}$ framework

Mikihiro Fujii, Yang Li

In the present paper, we consider the compressible Navier--Stokes--Korteweg system on the $2$ D whole plane and show that a unique global solution exists in the scaling critical Fou…

Large time behavior for solutions to the anisotropic Navier-Stokes equations in a 3D half-space

Mikihiro Fujii, Yang Li

We consider the large time behavior of the solution to the anisotropic Navier--Stokes equations in a $3$ D half-space. Investigating the precise anisotropic nature of linearized sol…

Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow

Mikihiro Fujii, Hiroyuki Tsurumi

In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $R^{2}$ . In [6], it was proved that the stationary N…

Stationary Navier--Stokes equations on the half spaces in the scaling critical framework

Mikihiro Fujii

In this paper, we consider the inhomogeneous Dirichlet boundary value problem for the stationary Navier--Stokes equations in $n$ -dimensional half spaces $\mathbb{R}^n_+= \{ x=(x',x…

Time-periodic solutions to the Navier--Stokes equations on the whole space including the two-dimensional case

Mikihiro Fujii

Let us consider the incompressible Navier--Stokes equations with the time-periodic external forces in the whole space $R^{n}$ with $n \geq 2$ and investigate the existence an…

Ill-posedness of the two-dimensional stationary Navier--Stokes equations on the whole plane

Mikihiro Fujii

We consider the two-dimensional stationary Navier--Stokes equations on the whole plane $R^{2}$ . In the higher-dimensional cases $R^{n}$ with $n ⩾ 3$ , the well…