jats:titleAbstract</jats:title>jats:pUsing 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 hyperviscosityjats:inline-formulajats:alternativesjats:tex-math$$(-\Delta )^{\theta }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:msupmml:mrowmml:mo(</mml:mo>mml:mo-</mml:mo>mml:miΔ</mml:mi>mml:mo)</mml:mo></mml:mrow>mml:miθ</mml:mi></mml:msup></mml:math></jats:alternatives></jats:inline-formula>, whenever the exponentjats:inline-formulajats:alternativesjats:tex-math$$\theta $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:miθ</mml:mi></mml:math></jats:alternatives></jats:inline-formula>is less than Lions’ exponent 5/4, i.e., whenjats:inline-formulajats:alternativesjats:tex-math$$\theta < 5/4$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:miθ</mml:mi>mml:mo<</mml:mo>mml:mn5</mml:mn>mml:mo/</mml:mo>mml:mn4</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>.</jats:p>