Student Probability Seminar

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Regularisation by noise and its limitations for the transport equation

Speaker: Andre Schenke, NYU Courant

Location: Warren Weaver Hall 202

Date: Wednesday, May 8, 2024, 12:30 p.m.

Synopsis:

We will review some results on well-posedness for the (deterministic and stochastic) transport equation. In particular we will sketch how adding noise to the equation can help us obtain better uniqueness results. 

Moreover, we will briefly talk about recent results with Stefano Modena on the limitations of this method. This means that if the drift term is too irregular, we have non-uniqueness in certain classes of solutions. This can be shown using the method of convex integration. So in this case, noise does not provide better uniqueness results than in the deterministic case.