619 citations · 1.6k across the 24 of their papers we have counts for
10 papers · 1 filter
Logarithmic Depletion of Vortex Stretching and Singularity Evasion in the 3D Navier-Stokes Equations
Zoran Grujic
We present a geometric-analytic mechanism for the suppression of finite-time singularities in the 3D incompressible (unforced) Navier-Stokes equations for critical point singularit…
Time-Global Regularity of the Navier-Stokes System with Hyper-Dissipation--Turbulent Scenario
Zoran Grujic, Liaosha Xu
The question of whether the hyper-dissipative (HD) Napier-Stokes (NS) system can exhibit spontaneous formation of singularities in the super-critical regime--the hyper-diffusion be…
Asymptotic Criticality of the Navier-Stokes Regularity Problem
Zoran Grujic, Liaosha Xu
The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fu…
A Regularity Criterion for Solutions to the 3D NSE in `Dynamically Restricted' Local Morrey Spaces
Zoran Grujic, Liaosha Xu
It is shown that a local-in-time strong solution to the 3D Navier-Stokes equations remains regular on an interval provided a smallness -condition on in a lower…
Local near-Beltrami structure and depletion of the nonlinearity in the 3D Navier-Stokes flows
Aseel Farhat, Zoran Grujic
Computational simulations of turbulent flows indicate that the regions of low dissipation/enstrophy production feature high degree of local alignment between the velocity and the v…
An algebraic reduction of the `scaling gap' in the Navier-Stokes regularity problem
Zachary Bradshaw, Aseel Farhat, Z. Grujic
It is shown--within a mathematical framework based on the suitably defined scale of sparseness of the super-level sets of the positive and negative parts of the vorticity component…