ABSTRACT
Flows in and TETSURO MIYAKAWA, Department of Mathematics, Kobe University
Rokko, Kobe 657-8501, JAPAN
1 Introduction
We are interested in the large-time asymptotic profiles of weak and strong solutions of
the Navier-Stokes system in the whole-space and in the half-space
Here, and when we impose the boundary condition
u=(u 1,…, u n ) and p denote, respectively, unknown velocity and pressure; a is a given initial velocity; and
We want to find asymptotic profiles of Navier-Stokes flows under some specific conditions on the initial velocities. In Section 2 we state our main results for flows in
The first result that, as t→∞, the solutions u admit an asymptotic expansion in terms of the space-time derivatives of Gaussian-like functions, provided the initial velocity a satisfies appropriate decay conditions and moment conditions. This improves a result of Carpio [2], in which is deduced the first-order asymptotics of two kinds, one in and the other in We show that one and the same result holds in all dimensions n≥2.
