28 citations · 131 across the 24 of their papers we have counts for
24 papers
Absence of local anomalous dissipation and local energy balance in 2D incompressible flows away from the boundary
Tobias Barker, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
For the 2D Navier-Stokes equations with no-slip boundary condition, we consider the issue of whether anomalous dissipation away from the boundary vanishes. In particular, we show t…
Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity
Tobias Barker, Pedro Gabriel Fernández-Dalgo, Christophe Prange
In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the…
On symmetry breaking for the Navier-Stokes equations
Tobias Barker, Christophe Prange, Jin Tan
Inspired by an open question by Chemin and Zhang about the regularity of the 3D Navier-Stokes equations with one initially small component, we investigate symmetry breaking and sym…
From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations
Tobias Barker, Christophe Prange
In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Som…
Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness
Dallas Albritton, Tobias Barker, Christophe Prange
We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary con…
Localized quantitative estimates and potential blow-up rates for the Navier-Stokes equations
Tobias Barker
We show that if is a smooth suitable weak solution to the Navier-Stokes equations on , that possesses a singular point …