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Navier-Stokes flow in the weighted Hardy space with applications to time decay problem. (English) Zbl 1346.35147
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.

##### MSC:
 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35C20 Asymptotic expansions of solutions to PDEs
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