We consider the barotropic Euler system describing the motion of a compressible
inviscid fluid driven by a stochastic forcing. Adapting the method of
convex integration we show that the initial value problem is ill-posed in
the class of weak (distributional) solutions. Specifically, we find a sequence
of
positive stopping times for which the Euler system admits infinitely many
solutions originating from the same initial data. The solutions are weak in the
PDE sense but strong in the probabilistic sense, meaning, they are defined
on an a priori given stochastic basis and adapted to the driving stochastic
process.
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