On stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise

2020/02/20 by Hao Tang, Tang, Hao · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2002.08719

openalex publication_date 2020/02/20 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28

Abstract

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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• Closed Estimates of Leray Projected Transport Noise and Strong Solutions of the Stochastic Euler Equations

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