Spatial decay of time-dependent incompressible navier-stokes flows with nonzero velocity at infinity

摘要

We consider the time-dependent Navier-Stokes system in a three-dimensional exterior domain with nonzero velocity at infinity. Under suitable assumptions on the data, it is shown that the velocity part of strong solutions, after subtraction of the far-field velocity, decays as (|x| (1 + |x| - x1)) -1, and its spatial gradient as (|x| (1 + |x| - x1)) -3/2, for |x| → ∞. The solution class in question includes solutions obtained by L2-variational methods and characterized by the fact that the velocity u and its spatial gradient Δxu are L∞(L2)-functions, and Δxu is additionally L2-integrable in time and in space.