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The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system
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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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Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations
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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