The probability perspective in supercritical deterministic problems


Many physical phenomena are modelled by (partial) differential equations. The mathematical analysis of these equations can, in nonlinear regimes, reveal highly complicated behaviors. From the study of the 3-bodies problem to theoretical fluid dynamics, such chaotic behaviors have led to a change of perspective that introduces the statistical approach as necessary. In this talk, we will present some regularization aspects of the statistical point of view for evolution equations. We will discuss mathematical models of fluid dynamics and nonlinear optics, exposing limitations of deterministic methods in their analysis. We then introduce probability frameworks that allow to overcome (in a statistical sense) such limitations and to establish well posedness and control on the evolution. We will also present a recent result obtained for the 3D incompressible Euler system using such a strategy. 


Zoom meeting room:

Meeting ID: 976 6762 6188

call to:976 6762 6188

Passcode: Zoominar