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math.AP2024★ 2 cited
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<-ΔS,ω\otimesω\right>=0, \end{equation*} where $S_{ij}=\frac{1}{2}\lef…
math.AP2024
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…