Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
Abstract
We study a non-isothermal model for incompressible magnetoviscoelastic fluids in ℝN, N=2,3, coupling the incompressible Navier-Stokes equations with the evolution equations for the deformation tensor, temperature, and magnetization. The material coefficients are allowed to depend on the temperature, and no artificial diffusion is imposed on the deformation tensor, leading to a coupled hyperbolic-parabolic system. We establish local well-posedness of strong solutions for sufficiently regular initial data and prove global existence for small perturbations of a constant equilibrium. The global analysis relies on a suitable auxiliary variable combining the velocity and the inverse deformation tensor, which reveals a hidden dissipative structure and allows us to derive uniform higher-order energy estimates for the coupled system.
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BibTeX
@misc{shao2026global,
title = {{Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion}},
author = {Yuanzhen Shao and Gieri Simonett},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32853},
eprint = {2609.32853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32853},
}
RIS
TY - UNPB
TI - Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
AU - Yuanzhen Shao
AU - Gieri Simonett
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32853
UR - https://arxiv.org/abs/2609.32853
AB - We study a non-isothermal model for incompressible magnetoviscoelastic fluids in ℝ^N, N=2,3, coupling the incompressible Navier-Stokes equations with the evolution equations for the deformation tensor, temperature, and magnetization. The material coefficients are allowed to depend on the temperature, and no artificial diffusion is imposed on the deformation tensor, leading to a coupled hyperbolic-parabolic system. We establish local well-posedness of strong solutions for sufficiently regular initial data and prove global existence for small perturbations of a constant equilibrium. The global analysis relies on a suitable auxiliary variable combining the velocity and the inverse deformation tensor, which reveals a hidden dissipative structure and allows us to derive uniform higher-order energy estimates for the coupled system.
ER -