Original version
Journal of Functional Analysis. 2023, 285 (9):110075, DOI: https://doi.org/10.1016/j.jfa.2023.110075
Abstract
The stochastic Euler-Poincaré equations with pseudo-differential/multiplicative noise are considered in this work. We first establish two new cancellation properties on pseudo-differential operators, which considerably extend the previous results for transport type noise only involving gradient operator. 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 is also studied for the multiplicative noise case.