A direct proof of the Caffarelli-Kohn-Nirenberg theorem

Jörg Wolf

Jörg Wolf

Banach Center Publications, Tome 83 (2008), p. 533-552 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $l i m s u p_{R \to 0 ⁺} 1 / R \int_{Q_{R} (x ₀, t ₀)} | c u r l u \times u / | u | | ² d x d t \leq ε_{*}$ for a sufficiently small $ε_{*} > 0$ .

Publié le : 2008-01-01

Zbl 1154.35426

EUDML-ID : urn:eudml:doc:282308

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     author = {J\"org Wolf},
     title = {A direct proof of the Caffarelli-Kohn-Nirenberg theorem},
     journal = {Banach Center Publications},
     volume = {83},
     year = {2008},
     pages = {533-552},
     zbl = {1154.35426},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-34}
}

Jörg Wolf. A direct proof of the Caffarelli-Kohn-Nirenberg theorem. Banach Center Publications, Tome 83 (2008) pp. 533-552. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-34/