Navier-Stokes flow in the weighted Hardy space with applications to time decay problem (Q285628)

The authors consider the Navier-Stokes (N-S) equations in \(\mathbb{R}^n\), \(n\geq 2\). They establish weighted estimates and \(m\)-th order asymptotic expansions of the N-S flow (\(m\in \mathbb{N}\)), under a moment condition on initial data. It is worth pointing out that the initial data can be chosen to be unbounded. In addition, the rapid time decay is established if the symmetry of the flow is assumed. The authors provide a clear comparison of their significant results with previous related ones.