8 citations · 35 across the 12 of their papers we have counts for
13 papers · 1 filter
Finite-time blowup for the Fourier-restricted Euler and hypodissipative Navier-Stokes model equations
Evan Miller
In this paper, we introduce the Fourier-restricted Euler and hypodissipative Navier--Stokes equations. These equations are analogous to the Euler and hypodissipative Navier--Stokes…
Growth rates for anti-parallel vortex tube Euler flows in three and higher dimensions
Stephen Gustafson, Evan Miller, Tai-Peng Tsai
We consider axisymmetric, swirl-free solutions of the Euler equations in three and higher dimensions, of generalized anti-parallel-vortex-tube-pair-type: the initial scalar vortici…
Finite-time blowup for the inviscid vortex stretching equation
Evan Miller
In this paper, we will introduce the inviscid vortex stretching equation, which is a model equation for the 3D Euler equation where the advection of vorticity is neglected. We will…
A Helmholtz-type decomposition for the space of symmetric matrices
Evan Miller, Eric Sawyer
In this paper, we introduce a Helmholtz-type decomposition for the space of square integrable, symmetric-matrix-valued functions analogous to the standard Helmholtz decomposition f…
A survey of geometric constraints on the blowup of solutions of the Navier--Stokes equation
Evan Miller
In this survey article, we will discuss some regularity criteria for the Navier--Stokes equation that provide geometric constraints on any possible finite-time blowup. We will also…
Finite-time blowup for smooth solutions of the Navier--Stokes equations on the whole space with linear growth at infinity
Evan Miller
In this paper we consider smooth solutions of the Navier--Stokes equations with a linear dependence on the spatial variable. We reduce the evolution of these solutions to a matrix…