Tuesday, June 30, 2020 - 15:15
Online Event
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Oberseminar Nonlinear Dynamics
It is a very classical yet still surprising result that noise can have a regularizing effect on differential equations. For example, adding a Brownian motion to an ODE with bounded and measurable vector field leads to a well posed equation with Lipschitz continuous flow. While the equation without noise may have none or many solutions. Classical proofs of such results are based on stochastic analysis and on the close link between the Brownian motion and the heat equation. In that derivation it is not obvious which property of the noise gives the regularization. A more recent approach by Catellier and Gubinelli leads to pathwise conditions under which regularization occurs. I will present a simplified version of their approach and use it to construct (very irregular) paths which are infinitely regularizing: after adding them to an ODE we have a unique solution and an infinitely smooth flow - even if the vector field is only a tempered distribution. This is joint work with Fabian Harang.
submitted by wartenberg (laura.wartenberg@wias-berlin.de, 030 20372539)