In this era of precision cosmology, a detailed physical understanding on the evolution of cosmic baryons is required. Cosmic magnetic fields, though still poorly understood, may represent an important component in the global cosmic energy flow that affects the baryon dynamics. We have developed an Eulerianbased cosmological magnetohydrodynamics code (CosmoMHD) with modern shock capturing scheme...

Parker problem in Hall magnetohydrodynamics (MHD) is considered. Poloidal shear into the toroidal flow generated by the Hall effect is incorporated. This is found to lead to a triple deck structure for the Parker problem in Hall MHD, with the magnetic field falling off in the intermediate Hall-resistive region more steeply (like 1/x) than that (like 1/x) in the outer ideal MHD region. ∗Permanen...

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions. Acknowledgements: The first and third authors wish to thank the hospitality of the Institut de Mathématiques de Toulouse, France, where this research has been car...

Isogeometric analysis (IGA) consists of using computer-aided design (CAD) models defining the geometry of the computational domain using both B-splines and nonuniform rational B-splines (NURBS) to represent the unknowns that are the solution of a partial differential equation using a finite element principle. In this paper, we review the main ideas of IGA and apply it to a reduced magnetohydrod...