A direct proof of the Caffarelli-Kohn-Nirenberg theorem

• Autorzy: Jörg Wolf
• Języki publikacji: EN

Abstrakty

EN

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 $ε_{*} > 0$.

Kategorie tematyczne

• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 533-552

Daty

wydano

2008

Twórcy

autor

Jörg Wolf

• Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

Identyfikatory

DOI

10.4064/bc81-0-34