Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in \(\mathbb{R}^n\) and \(\mathbb{R}_+^n\) (Q2771093)

The author investigates the large-time profiles of weak and strong solutions of the Navier-Stokes equations in the whole space \(\mathbb{R}^n\) and in the half-space \(\mathbb{R}^n_+\), \(n\geq 2\), under some specific conditions on the initial velocity. The main results are the following: As \(t\to \infty\), the solutions in the whole space admit an asymptotic expansion in terms of the space-time derivatives of Gaussian-like functions, provided the initial velocity satisfies decay and moment conditions. In the case of the half-space, the asymptotic expansion involves only the normal derivatives of the mentioned functions. An application of these results to the analysis of the modes of energy decay in the half-space is given.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00046].