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Non-uniqueness of weak solutions to hyperviscous Navier–Stokes equations: on sharpness of J.-L. Lions exponent


Using the convex integration technique for the three-dimensional Navier–Stokes equations introduced by Buckmaster and Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier–Stokes equations with fractional hyperviscosity (- Δ) θ, whenever the exponent θ is less than Lions’ exponent 5/4, i.e., when θ< 5 / 4.

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