超粘性Navier-斯托克斯方程弱解的非唯一性--关于J. - L.狮子指数
Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations -- On Sharpness of J.-L. Lions Exponent
摘要：
利用T. Buckmaster和V. Vicol的结果，证明了具有分数阶高粘性$(-Δ)^θ$的三维Navier-斯托克斯方程的非唯一弱解的存在性，当指数$θ$小于J. - L.狮子指数$5/4$，即，当$θ< 5/4$。
英文摘要：
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 $(-Δ)^θ$, whenever the exponent $θ$ is less than J.-L. Lions' exponent $5/4$, i.e., when $θ< 5/4$.
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