On the Dynamics of Ferrofluids: Global Weak Solutions to the Rosensweig System and Rigorous Convergence to Equilibrium
On the Dynamics of Ferrofluids: Global Weak Solutions to the Rosensweig System and Rigorous Convergence to Equilibrium
复制标题
铁磁流体动力学：Rosensweig 系统的全局弱解和平衡的严格收敛
DOI：
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发表时间：
2018
影响因子：
2
通讯作者：
F. Weber
中科院分区：
文献类型：
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作者：
R. Nochetto;K. Trivisa;F. Weber
本文建立了 Rosensweig 提出的铁磁流体动力学模型（Rosensweig，FerroHydrodynamics (1985)）弱解的全局存在性。该系统由线性动量守恒、不可压缩条件、角动量守恒和磁化强度演化来表示。存在性证明的灵感来自于重整化解的 DiPerna-Lions 理论。此外，还研究了铁流体动力学方程朝向准平衡的严格松弛极限。证明依赖于相对熵方法，该方法涉及构造合适的泛函，分析其时间演化并获得近似解序列的收敛结果。
This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (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.