Ryo Takada

Counterexamples of Commutator Estimates in the Besov and the Triebel–Lizorkin Spaces Related to the Euler Equations

This paper deals with the Kato–Ponce-type commutator estimates in the Besov space

Stability of time periodic solutions for the rotating navier-stokes equations

B^s_{p,q}(\mathbb{R}^n)

Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type

and the Triebel–Lizorkin space

Global solutions for the Navier-Stokes equations in the rotational framework

F^s_{p,q}(\mathbb{R}^n)

Dispersive estimates for the Navier-Stokes equations in the rotational framework

related to the Euler equations describing the motion of perfect incompressible fluids. We investigate the relation between the optimal bound of the commutator estimates and the solvability of the Euler equations. In particular, we show that these commutator estimates fail in

Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type

B^s_{p,q}(\mathbb{R}^n)

Strichartz estimates for the Euler equations in the rotational framework

and

Time periodic solutions to the Navier-Stokes equations in the rotational framework

F^s_{p,q}(\mathbb{R}^n)

Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force

with the critical differential order

On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity

s=n/p+1