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We consider the (barotropic) Euler system describing the motion of acompressible inviscid fluid driven by a stochastic forcing. Adapting the methodof convex integration we show that the initial value problem is ill-posed inthe class of weak (distributional) solutions. Specifically, we find a sequence$\tau_M \to \infty$ of positive stopping times for which the Euler systemadmits infinitely many solutions originating from the same initial data. Thesolutions are weak in the PDE sense but strong in the probabilistic sense,meaning, they are defined on an {\it a priori} given stochastic basis andadapted to the driving stochastic process.

On solvability and ill-posedness of the compressible Euler system subject to stochastic forces