6 papers · 1 filter
Finite-time blowup for the infinite dimensional vorticity equation
Evan Miller
In a previous work with Tai-Peng Tsai, the author studied the dynamics of axisymmetric, swirl-free Euler equation in four and higher dimensions. One conclusion of this analysis is…
On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
Evan Miller, Tai-Peng Tsai
In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension , axisymmetric, swirl-free sol…
Global regularity for axisymmetric, swirl-free solutions of the Euler equation in four dimensions
Evan Miller
In this paper, we prove global regularity for all smooth, axisymmetric, swirl-free solutions of the incompressible Euler equation in four dimensions. Previous works establishing gl…
On the interaction of strain and vorticity for solutions of the Navier--Stokes equation
Evan Miller
In this paper, we prove a new identity for divergence free vector fields, showing that \begin{equation*} \left<-ÎS,Ï\otimesÏ\right>=0, \end{equation*} where $S_{ij}=\frac{1}{2}\…
Singular, finite-time attractors for odd, smooth solutions of Burgers equation on the torus
Evan Miller
In this paper, we show that the positive multiples of a particular function -- which is singular with a jump discontinuity at the origin -- are finite-time global attractors in…
Permutation symmetric solutions of the incompressible Euler equation
Evan Miller
In this paper, we study permutation symmetric solutions of the incompressible Euler equation. We show that the dynamics of these solutions can be reduced to an evolution equation o…