Decay of Non-Stationary Navier-Stokes Flow with Nonzero Dirichlet Boundary Data

摘要

Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying vertical bar vertical bar v(t)vertical bar vertical bar(2) - 0 as t - infinity, and determine an upper bound for the decay rate.