Analysis of a Navier–Stokes phase-field crystal system

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-22 DOI:10.1016/j.nonrwa.2024.104263

Cecilia Cavaterra , Maurizio Grasselli , Muhammed Ali Mehmood , Riccardo Voso

引用次数: 0

Abstract

We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier–Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution.

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纳维-斯托克斯相场晶体系统分析

我们考虑了一个模拟悬浮在不可压缩流体中的胶体粒子流动的演化系统，并考虑了胶体结晶。该系统由体积平均速度的纳维-斯托克斯方程和密度偏差的所谓相场晶体方程组成。考虑到这一系统在周期域中的存在，并假设粘度和流动性取决于密度偏差，我们首先证明了三维中弱解的存在。然后，在二维中，我们确定了一个（唯一的）强解的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.