Wednesday, January 24, 2018 - 16:00 in V3-201
On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
A talk in the Bielefeld Stochastic Afternoon series by
Dominic Breit from Heriot-Watt University, Edinburgh
| Abstract: |
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 \(\tau_M \rightarrow \infty\) of positive stopping times for which the Euler system admits in 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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