On the existence and uniqueness of solution to a stochastic 2D Cahn-Hilliard-Navier-Stokes model
type: Item
instance of: scholarly article
title: On the existence and uniqueness of solution to a stochastic 2D Cahn-Hilliard-Navier-Stokes model
zbMATH Open document ID: 1365.35235
published in: Journal of Differential Equations
publication date: 2017-05-08T00:00:00Z
review text: Let \(M\) be a bounded domain in \(\mathbb R^2\) and let \(T>0\) be a constant. Consider the following stochastic Cahn-Hilliard-Navier-Stokes equation on \(M\times [0,T]\): \[ \begin{aligned} &\partial_t v-\theta_1\Delta v +(v\cdot \nabla)v+\nabla p- \kappa \mu \nabla \phi = g_1(t,v)+g_2(t,v)\dot W_t,\\ & \mathrm{div } v=0,\\ &\partial_t \phi +v\cdot \nabla \phi-\theta_3\mu=0,\\ &\mu=-\theta_2\Delta\phi +\alpha f(\phi),\end{aligned} \] where \(\theta_i,\kappa,\alpha\) are positive constants, \(W_t\) is a cylindrical Brwonian motion on a reference Hilbert space, \(g_i, f\) are suitable maps. Under suitable regularity and growth conditions on \(g_i\) and \(f\), the author proves the existence and uniqueness of variational solutions for the unknown velocity \(v=(v_1v_2)\) and order parameter \(\phi\).
reviewed by: Feng-Yu Wang
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 6712370
zbMATH Keywords: stochastic Cahn-Hilliard
zbMATH Keywords: Navier-Stokes
zbMATH Keywords: variational solutions
zbMATH Keywords: weak solutions
author: T. Tachim Medjo
MaRDI profile type: Publication
full work available at URL: j.jde.2017.03.008
OpenAlex ID: W2602757680
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DOI: 10.1016/J.JDE.2017.03.008
description: scientific article; zbMATH DE number 6712370