Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the half-space
This paper studies the behaviour as \(t\) tends to infinity of weak and strong solutions to the nonstationary incompressible Navier-Stokes system in the upper \(n\)-dimmensional real half-space. The aim is to find asymptotic profiles of Navier-Stokes flows under some specific conditions on the initial velocities. The main result (Theorem 3.5), which does not exhibit boundary effects, leads to an asymptotic expansion involving only the normal derivatives of Gaussian-like functions. The expansion is then applied to the analysis of the modes of energy decay of Navier-Stokes flows in the half-space, and it is proved the existence of a lower bound of rates of decay.
scientific article; zbMATH DE number 1757337