Yasunori Maekawa

A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

EXISTENCE OF ASYMMETRIC BURGERS VORTICES AND THEIR ASYMPTOTIC BEHAVIOR AT LARGE CIRCULATIONS

The asymmetric Burgers vortices are vortex solutions to the three dimensional stationary Navier-Stokes equations for viscous incompressible fluids in the presence of an asymmetric background straining flow. The asymmetry of the straining flow is expressed by a non-negative parameter less than

On Vorticity Formulation for Viscous Incompressible Flows in R + 3

1

On Isomorphism for the Space of Solenoidal Vector Fields and Its Application to the Incompressible Flows

. The Burgers vortices have been used as a model which expresses tube-like structures of concentrated vorticity fields in turbulence, and they are numerically well investigated especially in the case of large circulation numbers. However, their existence was proved mathematically only when either the asymmetry of the straining flow is not so strong or the circulation number is sufficiently small. In this paper we prove the existence of asymmetric Burgers vortices for all circulation numbers and each asymmetry parameter less than

Gevrey stability of Prandtl expansions for

1

2

. We also obtain their asymptotic expansion at large circulation numbers, which gives an explanation for a symmetrizing effect by a fast rotation.

-dimensional Navier–Stokes flows

In this paper we study the vorticity equations for viscous incompressible flows in the half space under the no-slip boundary condition on the velocity field. In particular, the boundary condition for the vorticity field is presented explicitly, and the solution formula for the linearized problem is obtained.

On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane

We consider the space of solenoidal vector fields in an unbounded domain

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

\Omega\subset \mathbb{R}^n

On the existence of Burgers vortices for high Reynolds numbers

whose boundary is given as a Lipschitz graph. It is shown that the space of solenoidal vector fields is isomorphic to the