We describe several aspects of an analytic/geometric framework for the three-dimensional Navier-Stokes regularity problem, which is directly inspired by the morphology of the regions of intense vorticity/velocity gradients observed in computational simulations of three-dimensional turbulence. Among these, we present a proof that the hyper-dissipative 3D Navier-Stokes are regular within an appropriate functional setting incorporating the intermittency in turbulent regimes, with any power of the Laplacian greater than 1.
Intermittency in turbulence and the 3D Navier-Stokes regularity problem*
Aseel Farhat, Florida State UniversityAuthors: Aseel Farhat, Zoran Grujic
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs