On stochastic Euler-Poincar\'{e} equations driven by pseudo-differential/multiplicative noise
Analysis of PDEs
2022-09-16 v4 Probability
Abstract
In this paper we focus on the stochastic Euler-Poincar\'{e} 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.
Keywords
Cite
@article{arxiv.2002.08719,
title = {On stochastic Euler-Poincar\'{e} equations driven by pseudo-differential/multiplicative noise},
author = {Hao Tang},
journal= {arXiv preprint arXiv:2002.08719},
year = {2022}
}