On the dynamics of ferrofluids: Global weak solutions to the Rosensweig\n system and rigorous convergence to equilibrium

2018/10/24 by Ricardo H. Nochetto, Nochetto, Ricardo H., Konstantina Trivisa +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1810.10691

openalex publication_date 2018/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article establishes the global existence of weak solutions to a model\nproposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics\nof ferrofluids. The system is expressed by the conservation of linear momentum,\nthe incompressibility condition, the conservation of angular momentum, and the\nevolution of the magnetization. The existence proof is inspired by the\nDiPerna-Lions theory of renormalized solutions. In addition, the rigorous\nrelaxation limit of the equations of ferrohydrodynamics towards the\nquasi-equilibrium is investigated. The proof relies on the relative entropy\nmethod, which involves constructing a suitable functional, analyzing its time\nevolution and obtaining convergence results for the sequence of approximating\nsolutions.\n

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