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pro vyhledávání: '"Miller, Evan"'
Autor:
Miller, Evan
In this paper, we prove a new identity for divergence free vector fields, showing that $\left<-\Delta S,\omega\otimes\omega\right>=0$. This identity will allow us to understand the interaction of different aspects of the nonlinearity in the Navier--S
Externí odkaz:
http://arxiv.org/abs/2407.02691
Autor:
Miller, Evan
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 on a single vorticity component $\omega_1$, and we characterize the rel
Externí odkaz:
http://arxiv.org/abs/2404.01505
Autor:
Miller, Evan
Quantiles can represent key operational and business metrics, but the computational challenges associated with inference has hampered their adoption in online experimentation. One-sample confidence intervals are trivial to construct; however, two-sam
Externí odkaz:
http://arxiv.org/abs/2401.10233
Autor:
Miller, Evan
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 equations respectively, but with the Helmholtz projection replaced by
Externí odkaz:
http://arxiv.org/abs/2307.03434
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 vorticity has a sign in the half-space, is odd under reflection across the pl
Externí odkaz:
http://arxiv.org/abs/2303.12043
Autor:
Miller, Evan
Publikováno v:
Nonlinearity. 36 (2023) 4086--4109
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 show that there are smooth solutions of this equation which blowup in
Externí odkaz:
http://arxiv.org/abs/2208.08974
Autor:
Miller, Evan
In this paper, we will discuss the axisymetric, swirl-free Euler equation in four and higher dimensions. We will show that in four and higher dimensions the axisymetric, swirl-free Euler equation has properties which could allow finite-time singulari
Externí odkaz:
http://arxiv.org/abs/2204.13406
Autor:
Miller, Evan, Sawyer, Eric
Publikováno v:
Trans. Amer. Math. Soc. Ser. B 10 (2023), 1449-1493
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 for vector fields. This decomposition provides a better understanding o
Externí odkaz:
http://arxiv.org/abs/2111.12891
Autor:
GOTBERG, BROOK E.1, MILLER, EVAN1
Publikováno v:
Denver Law Review. 2024, Vol. 101 Issue 4, p755-792. 38p.
Autor:
Miller, Evan
Publikováno v:
J. Elliptic Parabol. Equ. 7 (2021), no. 2, 589-599
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 discuss the physical significance of such regularity criteria.
Externí odkaz:
http://arxiv.org/abs/2111.00040