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

  • Author(s): Luo, Tianwen;
  • Titi, Edriss S
  • et al.
Abstract

AbstractUsing 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 $$(-\Delta )^{\theta }$$(-Δ)θ, whenever the exponent $$\theta $$θ is less than Lions’ exponent 5/4, i.e., when $$\theta < 5/4$$θ<5/4.

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