论文标题
随机幂律方程式全球概率强大的解决方案：存在和非唯一性
Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness
论文作者
论文摘要
我们关心的是由尺寸$ d \ geq3 $的加性随机强迫驱动的幂律流体。对于功率索引$ r \ in（1，\ frac {3d+2} {d+2}）$，我们在$ l^p_ {loc}中建立了无限的许多全球时间概率强，并且在分析上较弱的解决方案（[[0，\ infty）; l^2） c（[0，\ infty）; w^{1，\ max \ {1，r-1 \}}），p \ geq1 $对于$ l^2 \ 2 \ cap w^{1，\ max \ max \ {1，r-1，r-1，r-1 \}} $的每个散布初始条件的p \ geq1 $。该结果特别意味着法律上的非唯一性。如果$ r \ geq \ frac {3d+2} {d+2} $，则在三维情况下，我们的结果在三维情况下很敏锐。
We are concerned with the power-law fluids driven by an additive stochastic forcing in dimension $d\geq3$. For the power index $r\in(1,\frac{3d+2}{d+2})$, we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions in $L^p_{loc}([0,\infty);L^2)\cap C([0,\infty);W^{1,\max\{1,r-1\}}),p\geq1$ for every divergence free initial condition in $L^2\cap W^{1,\max\{1,r-1\}}$. This result in particular implies non-uniqueness in law. Our result is sharp in the three dimensional case in the sense that the solution is unique if $r\geq \frac{3d+2}{d+2}$.
