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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Bibliographic Details
Main Authors: Chengrong Zhang, Yajie Zhang
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
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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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).
ISSN:1029-242X