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.

## Published Web Location

https://doi.org/10.1007/s00526-020-01742-4
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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.