4 citations · 7 across the 3 of their papers we have counts for
7 papers
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…
On local Type I singularities of the Navier-Stokes equations and Liouville theorems
Dallas Albritton, Tobias Barker
We prove that suitable weak solutions of the Navier-Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying…
Existence and Weak* Stability for the Navier-Stokes System with Initial Values in Critical Besov Spaces
T. Barker
In 2016, Seregin and uSverák, conceived a notion of global in time solution (as well as proving existence of them) to the three dimensional Navier-Stokes equation with soleno…