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A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations
Peter Howard, Adam Larios, Quyuan Lin
We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it r…
Fractional Voigt-regularization of the 3D Navier--Stokes and Euler equations: Global well-posedness and limiting behavior
Zdzislaw Brzeźniak, Adam Larios, Isabel Safarik
The Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modificat…
Comparison of Coarsening Dynamics for the Cahn--Hilliard and Burgers--Cahn--Hilliard Equations
Peter Howard, Adam Larios, Quyuan Lin
We consider coarsening dynamics associated with a Burgers--Cahn--Hilliard system modeling a two-phase flow in one space dimension. Our emphasis is on the effect that coupling betwe…
A Note on Explicit Convergence Rates of Nonlocal Peridynamic Operators in -Norm
Adam Larios, Isabel Safarik
This note investigates the explicit convergence rates of nonlocal peridynamic operators to their classical (local) counterparts in -norm. Previous results used Fourier series…