24 citations · 31 across the 5 of their papers we have counts for
6 papers · 1 filter
Non-conservation of dimension in divergence-free solutions of passive and active scalar systems
Charles L. Fefferman, Benjamin C. Pooley, José L. Rodrigo
For any , we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in that weakly adve…
Asymptotics for vortex filaments using a modified Biot-Savart kernel
Benjamin C. Pooley, José L. Rodrigo
We consider a family of approximations to the Euler equations obtained by adding to the non-locality in the Biot-Savart kernel together with a mollification (with par…
Leray's fundamental work on the Navier-Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"
Wojciech S. Ożański, Benjamin C. Pooley
This article offers a modern perspective which exposes the many contributions of Leray in his celebrated work on the Navier--Stokes equations from 1934. Although the importance of…
Well-posedness for the diffusive 3D Burgers equations with initial data in
Benjamin C. Pooley, James C. Robinson
In this note we discuss the diffusive, vector-valued Burgers equations in a three-dimensional domain with periodic boundary conditions. We prove that given initial data in $H^{1/2}…
On a model for the Navier--Stokes equations using magnetization variables
Benjamin C. Pooley
It is known that in a classical setting, the Navier--Stokes equations can be reformulated in terms of so-called magnetization variables that satisfy \begin{equation}\label{Abs_…
An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces
Benjamin C. Pooley, James C. Robinson
In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-Lagrangian" form which involves the back-to-labels map (the inverse of the trajecto…