Paper Info
Title
On the Dynamics of Ferrofluids: Global Weak Solutions to the Rosensweig System and Rigorous Convergence to Equilibrium
Abstract
This article establishes the global existence of weak solutions to a model proposed by Rosensweig [Ferrohydrodynamics, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, 1985] for the dynamics of ferrofluids. The system is expressed by the conservation of linear momentum, the incompressibility condition, the conservation of angular momentum, and the evolution of the magnetization. The existence proof is inspired by the DiPerna-Lions theory of renormalized solutions. In addition, the rigorous relaxation limit of the equations of ferrohydrodynamics towards the quasi-equilibrium is investigated. The proof relies on the relative entropy method, which involves constructing a suitable functional, analyzing its time evolution, and obtaining convergence results for the sequence of approximating solutions.
Year
DOI
Venue
2019
10.1137/18M1224957
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
ferrofluids,hydrodynamic limit,magnetohydrodynamics,relaxation to equilibrium,relative entropy
Journal
51
Issue
ISSN
Citations 
6
0036-1410
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Ricardo H. Nochetto1907110.08
Konstantina Trivisa263.45
Franziska Weber300.34