Well-posedness of the transport equation by stochastic perturbation
speaker: Enrico Priola (Universita' di Torino)abstract: The talk is mainly about stochastic transport equation. In the first part I will present a result obtained with F. Flandoli and M. Gubinelli about well-posedness. We consider the linear transport equation with a globally H\"{o}lder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the deterministic PDE, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. The key tool is a differentiable stochastic flow constructed and analyzed by means of a special transformation of the drift of Ito-Tanaka type. In the second part of the talk I will discuss some recent results about existence of C1-solutions (opposite to what happens in the deterministic case where shocks may appear) and a stability property. Further developments of the main well-posedness result will be also given.
timetable:
Fri 24 May, 10:00 - 10:50, Aula Dini
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