Global existence and asymptotic behavior of self-similar solutions for the Navier-Stokes-Nernst-Planck-Poisson system in \(\mathbb R^3\)
type: Item
instance of: scholarly article
title: Global existence and asymptotic behavior of self-similar solutions for the Navier-Stokes-Nernst-Planck-Poisson system in \(\mathbb R^3\)
zbMATH Open document ID: 1234.35204
DOI: 10.1155/2011/329014
author: Chao Deng
author: Jihong Zhao
author: Shangbin Cui
published in: International Journal of Differential Equations
publication date: 2012-03-08T00:00:00Z
review text: Summary: We study the Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electrohydrodynamics. For small initial data, the global existence, uniqueness, and asymptotic stability as time goes to infinity of self-similar solutions to the Cauchy problem of this system posed in the whole three dimensional space are proved in the function spaces of pseudomeasure type.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6013182
Wikidata QID: Q58686751
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/329014
OpenAlex ID: W1978851734
cites work: Ill-posedness of the Navier-Stokes equations in a critical space in 3D
cites work: Q3593809
cites work: On the Navier-Stokes initial value problem. I
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: Well-posedness for the Navier-Stokes equations
cites work: Q4782579
cites work: The Debye system: existence and large time behavior of solutions
cites work: Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
cites work: On the basic equations for carrier transport in semiconductors
cites work: Scaling in nonlinear parabolic equations
cites work: Well-posedness for the drift-diffusion system in \(L^p\) arising from the semiconductor device simulation
cites work: The drift-diffusion system in two-dimensional critical Hardy space
cites work: ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION
cites work: ANALYTICAL APPROACHES TO CHARGE TRANSPORT IN A MOVING MEDIUM
cites work: ANALYSIS OF THE NAVIER–STOKES–NERNST–PLANCK–POISSON SYSTEM
cites work: Well-posedness of a dissipative system modeling electrohydrodynamics in Lebesgue spaces
cites work: One-point singular solutions to the Navier-Stokes equations
cites work: Global regular and singular solutions for a model of gravitating particles
cites work: Planar Navier-Stokes flow for singular initial data
cites work: Smooth or singular solutions to the Navier-Stokes system?
cites work: Stochastic cascades and 3-dimensional Navier-Stokes equations
cites work: Q5607484
cites work: The Navier-Stokes equations in the weak-\(L^n\) space with time-dependent external force
description: scientific article; zbMATH DE number 6013182