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The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system

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arxiv 1712.07015 v1 pith:ZCQI7OHX submitted 2017-12-19 math.AP

classification math.AP
keywords caffarelli-kohn-nirenberghyperdissipativenavier-stokesachievecorrespondingequationsextensiongeneralized
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We introduce a notion of suitable weak solution of the hyperdissipative Navier-Stokes equations and we achieve a corresponding extension of the regularity theory of Caffarelli-Kohn-Nirenberg.

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  1. Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations

    math.AP 2019-08 accept novelty 6.0 of 10

    Every 2D hypoviscous Navier-Stokes system with fractional Laplacian exponent theta below 1 admits nonunique C^0_t L^2_x weak solutions, including solutions with compact temporal support.

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