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Temporal and spatial decays for the Navier-Stokes equations. (English) Zbl 1076.35089
Summary: We obtain spatial and temporal decay rates of weak solutions of the Navier-Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by C. He and Z. Xin [Proc. R. Soc. Edinb., Sect. A, Math. 131, No. 3, 597–619 (2001; Zbl 0982.35083)] does not exceed $${3\over 2}$$. However, we show the power can be extended up to $${5\over 2}$$.

##### MSC:
 35Q30 Navier-Stokes equations 35B40 Asymptotic behavior of solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 35K05 Heat equation
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