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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2025-04-01
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| Series: | Journal of Inequalities and Applications |
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| 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). |
| format | Article |
| id | doaj-art-8fbcd3dec0e1434eaf4d8aae7d69ede0 |
| institution | DOAJ |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| 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 |