Nonuniform dependence for high-dimensional modified Euler–Poincaré system with multiplicative noises

In this paper, we consider the stochastically perturbed high-dimensional modified Euler–Poincaré system (SMEP2) on the torus [Formula: see text], [Formula: see text]. Based on the local well-posedness established in our recent work [L. Zhang, Effect of random noises on pathwise solutions to the high-dimensional modified Euler–Poincaré system, J. Differ. Equ. 403 (2024) 87–157], we further show that the data-to-solution mapping of the corresponding Cauchy problem is not uniformly continuous in the Sobolev spaces [Formula: see text] with [Formula: see text].