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In this paper we consider the regularity of weak solutions and find some regular criteria for 3D non-stationary Navier–Stokes equations. Moreover, we establish decay rates for weak solutions in general domains by means of the spectral decomposition method of fractional powers of the Stokes operator.
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Pigong Han, Regularity and decay properties of weak solutions to Navier–Stokes equations in general domains. Port. Math. 67 (2010), no. 1, pp. 57–74DOI 10.4171/PM/1857