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

2023/06/28 by Hao Tang · 2 citations
Engineering · Economics, Econometrics and Finance · Computer Science · #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering

paper · doi: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.

Citations

• Global existence, blow-up and stability for a stochastic transport equation with non-local velocity

Cited by

• Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
• Closed Estimates of Leray Projected Transport Noise and Strong Solutions of the Stochastic Euler Equations

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