论文标题
在由伪差异/乘法噪声驱动的随机Euler-Poincaré方程上
On stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise
论文作者
论文摘要
在本文中，我们关注具有伪分别/乘法噪声的随机欧拉峰方程。我们首先在伪差异操作员上建立了两个新的取消属性，这些属性在能量估计中起着关键作用。然后，我们获得有关局部解决方案，爆破标准和全球存在的结果。还研究了在退出时间上的稳定性与解决方案对初始数据的连续依赖性之间的相互作用，以用于乘法噪声案例。
In this paper we focus on the stochastic Euler-Poincaré equations with pseudo-differential/multiplicative noise. We first establish two new cancellation properties on pseudo-differential operators, which play a key role in energy estimate. Then, we obtain results on local solution, blow-up criterion and global existence. The interplay between stability on exiting times and continuous dependence of solution on initial data are also studied for the multiplicative noise case.
