The stochastic 3D globally modified Navier-Stokes equations: existence, uniqueness and asymptotic behavior
type: Item
instance of: scholarly article
title: The stochastic 3D globally modified Navier-Stokes equations: existence, uniqueness and asymptotic behavior
zbMATH Open document ID: 1443.35205
published in: Communications on Pure and Applied Analysis
publication date: 2018-08-23T00:00:00Z
review text: The main results of the paper under review are related to the stochastic system of globally modified Navier-Stokes equations \[ \begin{cases} du(t)=[\nu\Delta u -F_N(\Vert u\Vert)[(u.\nabla) u]+\nabla p-F(u)]dt +\sum_{k=1}^\infty \sigma_k(u(t))d W_k(t) \\ \nabla.u=0\text{ in }(0,T)\times\mathcal{M} \\ u=0\text{ on }(0,T)\times\Gamma \\ u(0,x)=u_0(x),\ x\in\mathcal{M} \end{cases} \] where \((W_k)_{k\ge 1}\) is a sequence of independent one-dimensional standard Brownian motions, \(F_N(r)=\min\{1,N/r\}\), and \(\mathcal{M}\subseteq\mathbb{R}^3\) is a bounded domain with smooth boundary. For the above system, under suitable conditions, one proves the existence of a unique strong solution. One also studies the convergence of the strong solution for \(N\to\infty\), and one then proves proves the existence of a martingale solution.
reviewed by: Daniel Beltiţă
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: 6923959
zbMATH Keywords: globally modfied Navier-Stokes equations
zbMATH Keywords: stochastic equations
zbMATH Keywords: strong solutions
zbMATH Keywords: stability
author: Gabriel Deugoué
author: T. Tachim Medjo
MaRDI profile type: Publication
full work available at URL: cpaa.2018123
OpenAlex ID: W2806662049
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Wikidata QID: Q129689886
DOI: 10.3934/CPAA.2018123
description: scientific article; zbMATH DE number 6923959