Temporal and spatial decays for the Navier-Stokes equations. (English) Zbl 1076.35089

Bae, Hyeong-Ohk; Jin, Bum Ja

Proc. R. Soc. Edinb., Sect. A, Math. 135, No. 3, 461-477 (2005).

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

Keywords:

heat equation; Navier-Stokes equation; decay rates; weak solutions; strong solutions