Stability of the two-dimensional complex fluid model in a slab domain

Abstract In this paper, we focus on a two-dimensional (2D) complex fluid model in a slab domain. Based on time-weighted energy estimates, we work in Eulerian coordinates to establish the stability and algebraical decay-in-time behavior near hydrostatic equilibrium of the 2D complex fluid model with...

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Main Authors: Chengrong Zhang, Yajie Zhang
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:https://doi.org/10.1186/s13660-025-03301-x
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author Chengrong Zhang
Yajie Zhang
author_facet Chengrong Zhang
Yajie Zhang
author_sort Chengrong Zhang
collection DOAJ
description Abstract In this paper, we focus on a two-dimensional (2D) complex fluid model in a slab domain. Based on time-weighted energy estimates, we work in Eulerian coordinates to establish the stability and algebraical decay-in-time behavior near hydrostatic equilibrium of the 2D complex fluid model with Navier(-slip) boundary condition. Since the 2D complex fluid model can be obtained from the equations of 2D incompressible nonresistive magnetohydrodynamic (MHD) fluids by a transformation of the stream function, as a byproduct, we also obtain the stability and the algebraical decay-in-time behavior of the 2D incompressible nonresistive MHD equations with an impressed horizontal magnetic field in a slab domain. Our results enrich the small perturbation theory in both the complex fluid model in (Lin and Zhang in Arch. Ration. Mech. Anal. 216: 905–920, 2015) and the nonresistive MHD equations in (Ren et al. in Nonlinearity 29:1257, 2016).
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issn 1029-242X
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publishDate 2025-04-01
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series Journal of Inequalities and Applications
spelling doaj-art-8fbcd3dec0e1434eaf4d8aae7d69ede02025-08-20T03:18:34ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-04-012025111810.1186/s13660-025-03301-xStability of the two-dimensional complex fluid model in a slab domainChengrong Zhang0Yajie Zhang1College of Mathematics and Statistics, Fuzhou UniversityInstitute of Applied Physics and Computational MathematicsAbstract In this paper, we focus on a two-dimensional (2D) complex fluid model in a slab domain. Based on time-weighted energy estimates, we work in Eulerian coordinates to establish the stability and algebraical decay-in-time behavior near hydrostatic equilibrium of the 2D complex fluid model with Navier(-slip) boundary condition. Since the 2D complex fluid model can be obtained from the equations of 2D incompressible nonresistive magnetohydrodynamic (MHD) fluids by a transformation of the stream function, as a byproduct, we also obtain the stability and the algebraical decay-in-time behavior of the 2D incompressible nonresistive MHD equations with an impressed horizontal magnetic field in a slab domain. Our results enrich the small perturbation theory in both the complex fluid model in (Lin and Zhang in Arch. Ration. Mech. Anal. 216: 905–920, 2015) and the nonresistive MHD equations in (Ren et al. in Nonlinearity 29:1257, 2016).https://doi.org/10.1186/s13660-025-03301-xComplex fluid modelTime-weighted energy estimatesNonresistive viscous MHD fluidsStabilityAlgebraical decay-in-time
spellingShingle Chengrong Zhang
Yajie Zhang
Stability of the two-dimensional complex fluid model in a slab domain
Journal of Inequalities and Applications
Complex fluid model
Time-weighted energy estimates
Nonresistive viscous MHD fluids
Stability
Algebraical decay-in-time
title Stability of the two-dimensional complex fluid model in a slab domain
title_full Stability of the two-dimensional complex fluid model in a slab domain
title_fullStr Stability of the two-dimensional complex fluid model in a slab domain
title_full_unstemmed Stability of the two-dimensional complex fluid model in a slab domain
title_short Stability of the two-dimensional complex fluid model in a slab domain
title_sort stability of the two dimensional complex fluid model in a slab domain
topic Complex fluid model
Time-weighted energy estimates
Nonresistive viscous MHD fluids
Stability
Algebraical decay-in-time
url https://doi.org/10.1186/s13660-025-03301-x
work_keys_str_mv AT chengrongzhang stabilityofthetwodimensionalcomplexfluidmodelinaslabdomain
AT yajiezhang stabilityofthetwodimensionalcomplexfluidmodelinaslabdomain