3 papers
math.AP2026
Quantitative estimates for the forced Navier-Stokes equations and applications
Tobias Barker, Henry Popkin
In this paper, we prove a localisation of a slightly supercritical (Orlicz) regularity criterion for the 3D incompressible Navier-Stokes equations. This is a refinement to the rece…
math.AP2026
Quantitative classification of potential Navier-Stokes singularities beyond the blow-up time
Tobias Barker
In \cite{hou}, Hou gave a compelling numerical candidate for a singular solution of the 3D Navier-Stokes equations. We pioneer classifications of potentially singular solutions, mo…
math.AP2024
Critical norm blow-up rates for the energy supercritical nonlinear heat equation
Tobias Barker, Hideyuki Miura, Jin Takahashi
We prove the first classification of blow-up rates of the critical norm for solutions of the energy supercritical nonlinear heat equation, without any assumptions such as radial sy…