Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations

Abstract We establish the global well-posedness of the axisymmetric solutions to the incompressible viscous Hall-magnetohydrodynamic equations.

[1]  Jean Leray,et al.  Sur le mouvement d'un liquide visqueux emplissant l'espace , 1934 .

[2]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .

[3]  R. A. Silverman,et al.  The Mathematical Theory of Viscous Incompressible Flow , 1972 .

[4]  Dongho Chae,et al.  On the temporal decay for the Hall-magnetohydrodynamic equations , 2013, 1302.4601.

[5]  E. Titi,et al.  Invariant helical subspaces for the Navier-Stokes equations , 1990 .

[6]  Zhen Lei On axially symmetric incompressible magnetohydrodynamics in three dimensions , 2012, 1212.5968.

[7]  M. Lighthill,et al.  Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions , 1960, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  Milan Pokorný,et al.  On Axially Symmetric Flows in $mathbb R^3$ , 1999 .

[9]  Tosio Kato,et al.  Commutator estimates and the euler and navier‐stokes equations , 1988 .

[10]  X. Moussas,et al.  A review of magneto-vorticity induction in Hall-MHD plasmas , 2001 .

[11]  Pierre Degond,et al.  Well-posedness for Hall-magnetohydrodynamics , 2012, 1212.3919.

[12]  Jian-Guo Liu,et al.  Characterization and Regularity for Axisymmetric Solenoidal Vector Fields with Application to Navier-Stokes Equation , 2009, SIAM J. Math. Anal..

[13]  H. Abidi Résultats de régularité de solutions axisymétriques pour le système de Navier–Stokes , 2008 .

[14]  Pierre Degond,et al.  Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system , 2011 .

[15]  M. R. Ukhovskii,et al.  Axially symmetric flows of ideal and viscous fluids filling the whole space , 1968 .