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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03301-x |
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| Summary: | 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 |