Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, February 14, 2022 - 16:00 to 17:00
Location: 
on Zoom

Speaker Info

Institution: 
Carnegie Mellon University
Abstract: 

The deterministic Navier-Stokes equations describe the motion of viscous Newtonian fluids. In this presentation, we discuss the Navier-Stokes equations driven by cylindrical white noise. This model arises when physical, empirical, numerical, and experimental uncertainties during the flow evolution are considered. We are interested in existence, pathwise uniqueness, and energy estimates of probabilistically strong solutions to the stochastic Navier-Stokes equations.

We place the equation on the three-dimensional torus. If the equation is deterministic and if the initial datum has a sufficiently small L^p norm (p>3), the solution is known to exist globally in the same L^p space. If transferring this problem to a stochastic setting, then one would encounter many challenges. In this presentation, I will explain the techniques we used to address these challenges, including the nonlinear term, the multiplicative noise, and the non-uniform smallness of initial data in the probability space.