4 citations · 7 across the 5 of their papers we have counts for
10 papers · 1 filter
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…
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 …
Local Hadamard well-posedness results for the Navier-Stokes equations
Tobias Barker
In this paper we consider classes of initial data that ensure local-in-time Hadamard well-posedness of the associated weak Leray-Hopf solutions of the three-dimensional Navier-Stok…
Scale-invariant estimates and vorticity alignment for Navier-Stokes in the half-space with no-slip boundary conditions
Tobias Barker, Christophe Prange
This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in with no-slip boundary condition, with the assumption th…
Localized smoothing for the Navier-Stokes equations and concentration of critical norms near singularities
Tobias Barker, Christophe Prange
This paper is concerned with two dual aspects of the regularity question of the Navier-Stokes equations. First, we prove a local in time localized smoothing effect for local energy…
Localised necessary conditions for singularity formation in the Navier-Stokes equations with curved boundary
Dallas Albritton, Tobias Barker
We generalize two results in the Navier-Stokes regularity theory whose proofs rely on `zooming in' on a presumed singularity to the local setting near a curved portion $Γ\subset \p…