Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
Year: 2026
Type: preprint
Abstract: We study a non-isothermal model for incompressible magnetoviscoelastic fluids in $\mathbb{R}^N$, $N=2,3$, 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.
Source: arXiv (Cornell University)
Authors: Shao, Yuanzhen, Simonett, Gieri
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: Collaborative Research: On calculating polar solvation and binding energies for non-rigid proteins in the Poisson-Boltzmann theory: modeling, analysis and application, Collaborative Research: A new diffuse-interface approach to ensemble average solvation energy: modeling, analysis and computation
OpenAlex ID: W7214741563