2024/12/06 by N. Vinod, Thanh Tran, Vinod, Noah +1
Earth and Planetary Sciences · Engineering · Environmental Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #Hydrocarbon exploration and reservoir analysis #Methane Hydrates and Related Phenomena #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2412.04753
openalex publication_date 2024/12/06 · openalex created_date 2024/12/10 · openalex updated_date 2026/07/28
Ferromagnetic magnetohydrodynamics concerns the study of conducting fluids with intrinsic magnetisation under the influence of a magnetic field. It is a generalisation of the magnetohydrodynamical equations and takes into account the dynamics of the magnetisation of a fluid. First proposed by Lingam (Lingam, `Dissipative effects in magnetohydrodynamical models with intrinsic magnetisation', Communications in Nonlinear Science and Numerical Simulation Vol 28, pp 223-231, 2015), the usual equations of magnetohydrodynamics, namely the Navier-Stokes equation and the induction equation, are coupled with the Landau-Lifshitz-Gilbert equation. In this paper, the local existence, uniqueness and regularity of weak solutions to this system are discussed.