Two regularity criteria for the 3D MHD equations [PDF]
arXiv, 2009 This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one-direction while the second one requires suitable boundedness of the derivative of the pressure in one-direction.
arxiv
Ten-moment two-fluid plasma model agrees well with PIC/Vlasov in GEM problem [PDF]
arXiv, 2010 We simulate magnetic reconnection in the GEM problem using a two-fluid model with 10 moments for the electron fluid as well as the proton fluid. We show that use of 10 moments for electrons gives good qualitative agreement with the the electron pressure tensor components in published kinetic simulations.
arxiv
Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows [PDF]
arXiv, 2011 In this paper we consider the equations of the unsteady viscous, incompressible, and heat conducting magnetohydrodynamic flows in a bounded three-dimensional domain with Lipschitz boundary. By an approximation scheme and a weak convergence method, the existence of a weak solution to the three-dimensional density dependent generalized incompressible ...
arxiv
Global small solution to the 2D MHD system with a velocity damping term [PDF]
arXiv, 2013 This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state.
arxiv
Regularity criteria for the 3D MHD equations in term of velocity [PDF]
arXiv, 2013 In this paper we consider three-dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving the fractional derivative of velocity in one direction, which generalize some known results.
arxiv
On the construction of solutions to the free-surface incompressible ideal magnetohydrodynamic equations [PDF]
arXiv, 2016 We consider a free boundary problem for the incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. The magnetic field is tangent and the total pressure vanishes along the plasma-vacuum interface. Under the Taylor sign condition of the total pressure on the free surface, we prove the local well-posedness of
arxiv
Well-posedness and blowup of 1D electron magnetohydrodynamics [PDF]
arXivThe one-dimensional toy models proposed for the three-dimensional electron magnetohydrodynamics in our previous work share some similarities with the original dynamics under certain symmetry. We continue to study the well-posedness issue and explore the potential singularity formation scenario for these models.
arxiv
Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$ [PDF]
arXiv, 2017 We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2$. The previously known local well-posedness space was $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2+1$. Thus the result presented here is an improvement.
arxiv
On a spectral problem in magnetohydrodynamics and its relevance for the geodynamo [PDF]
arXiv, 2018 One of the most remarkable features of the geodynamo is the irregular occurrence of magnetic field reversals. Starting with the operator theoretical treatment of a non-selfadjoint dynamo operator, we elaborate a dynamical picture of those reversals that rely on the existence of exceptional spectral points.
arxiv
On uniqueness and helicity conservation of weak solutions to the electron-MHD system [PDF]
arXiv, 2019 We study the weak solutions to the electron-MHD system and obtain a conditional uniqueness result. In addition, we prove conservation of helicity for weak solutions to the electron-MHD system under a geometric condition.
arxiv