An estimate for the vorticity of the Navier�Stokes equation (original) (raw)

Data Revues 1631073x V347i1 2 S1631073x08003270, 2009

Abstract

Let u→(⋅,t) be a strong solution of the Navier–Stokes equation on 3-dimensional torus T3, and ω→(⋅,t)=∇×u→(⋅,t) be the vorticity. In this Note we show that‖ω→(⋅,t)‖1+24ν‖u→(⋅,t)‖22 is decreasing in t as long as the solution u→(⋅,t) exists, where ν>0 is the viscosity constant and ‖⋅‖q denotes the Lq-norm. To cite this article: Z. Qian, C. R. Acad. Sci. Paris, Ser. I

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