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On stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise
Hao Tang · 2020-02-20 · via math.PR updates on arXiv.org

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.

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