Hideyuki Miura

Asymptotics of Small Exterior Navier-Stokes Flows with Non-Decaying Boundary Data

We prove the existence of unique solutions for the 3D incompressible Navier-Stokes equations in an exterior domain with small boundary data which do not necessarily decay in time. As a corollary, the existence of unique small time-periodic solutions is shown. We next show that the spatial asymptotics of the periodic solution is given by the same Landau solution at all times. Lastly we show that if the boundary datum is time-periodic and the initial datum is asymptotically self-similar, then the solution converges to the sum of a time-periodic vector field and a forward self-similar vector field as time goes to infinity.

Remark on Single Exponential Bound of the Vorticity Gradient for the Two-Dimensional Euler Flow Around a Corner

In this paper, we consider the two–dimensional Euler flow under a simple symmetry condition, with hyperbolic structure in a unit square

On Vorticity Directions near Singularities for the Navier-Stokes Flows with Infinite Energy

{D = \{(x_1,x_2):0 < x_1+x_2 < \sqrt{2},0 < -x_1+x_2 < \sqrt{2}\}}

Remark on the Helmholtz decomposition in domains with noncompact boundary

D={(x1,x2):0<x1+x2<2,0<-x1+x2<2}. It is shown that the Lipschitz estimate of the vorticity on the boundary is at most a single exponential growth near the stagnation point.

On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions

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

On fundamental solutions for non-local parabolic equations with divergence free drift

\Omega\subset \mathbb{R}^n

Point Singularities of 3D Stationary Navier–Stokes Flows

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

The growth of the vorticity gradient for the two-dimensional Euler flows on domains with corners

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