Work

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

Year: 2025

Type: article

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).

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-025-03301-x

Authors: Chengrong Zhang, Yajie Zhang

Institutions: Fuzhou University, Institute of Applied Physics and Computational Mathematics

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funders: National Natural Science Foundation of China, Natural Science Foundation of Fujian Province