Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations -- On Sharpness of J.-L. Lions Exponent
Open Access Publications from the University of California

## 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

Using the convex integration technique for the three-dimensional Navier-Stokes equations introduced by T. Buckmaster and V. Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier-Stokes equations with fractional hyperviscosity $(-\Delta)^{\theta}$, whenever the exponent $\theta$ is less than J.-L. Lions' exponent $5/4$, i.e., when $\theta < 5/4$.

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