Shin'ya Matsui

Global Existence of Two-Dimensional Navier—Stokes Flow with Nondecaying Initial Velocity

Abstract. A global-in-time unique smooth solution is constructed for the Cauchy problem of the Navier—Stokes equations in the plane when initial velocity field is merely bounded not necessary square-integrable. The proof is based on a uniform bound for the vorticity which is only valid for planar flows. The uniform bound for the vorticity yields a coarse globally-in-time a priori estimate for the maximum norm of the velocity which is enough to extend a local solution. A global existence of solution for a q-th integrable initial velocity field is also established when

On estimates in Hardy spaces for the Stokes flow in a half space

q > 2

On blow-up rate for sign-changing solutions in a convex domain

.

Note on an example of a zero viscosity limit for Navier-Stokes flows with the initial boundary layer in the disk

Since

Blow up rate for semilinear heat equations with subcritical nonlinearity

u=e^{-tA}u_{0}

On blow up rate for sign-changing solutions in a convex domain

and

Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force

||A^{1/2}u||_{2}=||\nabla u||_{2},

Blow up rate for semilinear heat equation with subcritical nonlinearity

(2) follows for

Navier-Stokes Equations in a Rotating Frame in

p=2.(\mathrm{S}\mathrm{e}\mathrm{e}

{\mathbb R}^3

Borchers and Miyakawa [3] for applications.) For