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A direct proof of the Caffarelli-Kohn-Nirenberg theorem

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Wolf J.

Banach Center Publications

2008

tom 81

nr 1

533-552

In the present paper we give a new proof of the Caffarelli-Kohn-Nirenberg theorem based on a direct approach. Given a pair (u,p) of suitable weak solutions to the Navier-Stokes equations in ℝ³ × ]0,∞[ the velocity field u satisfies the following property of partial regularity: The velocity u is Lipschitz continuous in a neighbourhood of a point (x₀,t₀) ∈ Ω × ]0,∞ [ if $lim sup_{R→0⁺} 1/R ∫_{Q_R(x₀,t₀)} |curl u × u/|u| |² dx dt ≤ ε_{*}$ for a sufficiently small $ε_{*} > 0$.

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1 Banach Center Publications

1 Wolf J.

1 2008

Wyniki wyszukiwania

A direct proof of the Caffarelli-Kohn-Nirenberg theorem