论文信息 - A regularity criterion for the solutions of 3D Navier–Stokes equations

A regularity criterion for the solutions of 3D Navier–Stokes equations

Abstract In terms of two partial derivatives of any two components of velocity fields, we give a new criterion for the regularity of solutions of the Navier–Stokes equation in R 3 . More precisely, let u = ( u 1 , u 2 , u 3 ) be a weak solution in ( 0 , T ) × R 3 . Then u becomes a classical solution if any two functions of ∂ 1 u 1 , ∂ 2 u 2 and ∂ 3 u 3 belong to L θ ( 0 , T ; L r ( R 3 ) ) provided with 2 θ + 3 r = 2 , 3 2 r ⩽ ∞ .

Xicheng Zhang | Xicheng Zhang

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