论文标题
对称随机的时间规律性$ p $ - 斯托克斯系统
Temporal regularity of symmetric stochastic $p$-Stokes systems
论文作者
论文摘要
我们在一个有限的域中研究对称的随机$ p $ - 斯托克斯系统，$ p \ in（1，\ infty）$。结果是双重的。 首先，我们表明，在分析较弱的解决方案的背景下，随机压力与非发育不良随机力有关 - 在BESOV量表上享有近$ -1/2 $的时间导数。 其次，我们验证了强质解决方案的速度组件〜$ u $ $ u $在指数尼古尔斯基空间中遵守$ 1/2 $的时间导数。此外，我们证明了非线性对称梯度$ V（\ varepsilon u）=（κ+ | \ varepsilon u |）
We study the symmetric stochastic $p$-Stokes system, $p \in (1,\infty)$, in a bounded domain. The results are two-folded. First, we show that in the context of analytically weak solutions the stochastic pressure -- related to non-divergence free stochastic forces -- enjoys almost $-1/2$ temporal derivatives on a Besov scale. Second, we verify that the velocity component~$u$ of strong solutions obeys $1/2$ temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient $V(\varepsilon u) = (κ+ |\varepsilon u|)^{(p-2)/2} \varepsilon u$, $κ\geq 0$, has $1/2$ temporal derivatives in a Nikolskii space.
