论文标题
不可独特的权力流动
Non Uniqueness of power-law flows
论文作者
论文摘要
我们应用凸集成的技术来获得幂律流体的非唯一性和存在结果，尺寸为$ d \ ge 2 $。对于低于紧凑型阈值的功率索引$ q $，即（1，\ frac {2d} {d+2}）$ in（1，\ frac {2d} {d+2}）$，我们显示了Leray-Hopf解决方案的不适。对于（1，\ frac {3d+2} {d+2}）$ in（1，\ frac {d+2}）$的较宽类别的索引$ q \，我们显示了分布（非Leray-Hopf）解决方案的不适性，从而扩大了Buckmaster和VICOL的开创性纸张。在这个更广泛的类中，我们还为$ l^2 $中的每个基准构建了非唯一解决方案。
We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension $d\ge 2$. For the power index $q$ below the compactness threshold, i.e. $q \in (1, \frac{2d}{d+2})$, we show ill-posedness of Leray-Hopf solutions. For a wider class of indices $q \in (1, \frac{3d+2}{d+2})$ we show ill-posedness of distributional (non-Leray-Hopf) solutions, extending the seminal paper of Buckmaster and Vicol. In this wider class we also construct non-unique solutions for every datum in $L^2$.
