Special Session 168: Stochastic Analysis and Large Scale Interacting Systems

Remarks on the three-dimensional Navier-Stokes equations with Lions` exponent forced by space-time white noise
Kazuo Yamazaki
University of Nebraska-Lincoln
USA
Co-Author(s):    
Abstract:
Navier-Stokes equations forced by space-time white becomes singular in a way that in all dimensions equal to or higher than two, the product of the nonlinear term becomes ill-defined. In case dimension is two, Da Prato-Debussche proved its global solution theory using explicit knowledge of invariant measure. More recently, Hairer-Rosati developed a new way to prove its global solution theory without relying on invariant measure. We apply the latter approach to the three-dimensional Navier-Stokes equations forced by space-time white noise and energy-critical diffusion; despite the absence of any knowledge of its invariant measure, we prove its global solution theory.