We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resistive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions.
Keywords: Hall-MHD, Smooth solutions, Well-posedness, Liouville theorem
@article{AIHPC_2014__31_3_555_0, author = {Chae, Dongho and Degond, Pierre and Liu, Jian-Guo}, title = {Well-posedness for {Hall-magnetohydrodynamics}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {555--565}, publisher = {Elsevier}, volume = {31}, number = {3}, year = {2014}, doi = {10.1016/j.anihpc.2013.04.006}, mrnumber = {3208454}, zbl = {1297.35064}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.006/} }
TY - JOUR AU - Chae, Dongho AU - Degond, Pierre AU - Liu, Jian-Guo TI - Well-posedness for Hall-magnetohydrodynamics JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 555 EP - 565 VL - 31 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.006/ DO - 10.1016/j.anihpc.2013.04.006 LA - en ID - AIHPC_2014__31_3_555_0 ER -
%0 Journal Article %A Chae, Dongho %A Degond, Pierre %A Liu, Jian-Guo %T Well-posedness for Hall-magnetohydrodynamics %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 555-565 %V 31 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.006/ %R 10.1016/j.anihpc.2013.04.006 %G en %F AIHPC_2014__31_3_555_0
Chae, Dongho; Degond, Pierre; Liu, Jian-Guo. Well-posedness for Hall-magnetohydrodynamics. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 3, pp. 555-565. doi : 10.1016/j.anihpc.2013.04.006. http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.006/
[1] Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinet. Relat. Models 4 (2011), 901 -918 | MR | Zbl
, , , ,[2] Linear analysis of the Hall effect in protostellar disks, Astrophys. J. 552 (2001), 235 -247
, ,[3] On hydromagnetic waves in atmospheres with application to the sun, Theor. Comput. Fluid Dyn. 10 (1998), 37 -70 | Zbl
,[4] Nonlinear stability of a Vlasov equation for magnetic plasmas, Kinet. Relat. Models 6 (2013), 269 -290 | MR | Zbl
, , , ,[5] Perfect Incompressible Fluids, Clarendon Press, Oxford (1998) | MR
,[6] Inéquations en thermoélasticité et magnétohydrodynamique, Arch. Ration. Mech. Anal. 46 (1972), 241 -279 | MR | Zbl
, ,[7] Magnetic reconnection in solar flares, Geophys. Astrophys. Fluid Dyn. 62 (1991), 15 -36
,[8] An Introduction to the Mathematical Theory of the Navier–Stokes Equations, vol. II, Springer (1994) | MR | Zbl
,[9] Bifurcation analysis of magnetic reconnection in Hall-MHD systems, Phys. D 208 (2005), 59 -72 | MR | Zbl
, ,[10] Studies on magneto-hydrodynamic waves and other anisotropic wave motions, Philos. Trans. R. Soc. Lond. Ser. A 252 (1960), 397 -430 | MR | Zbl
,[11] Vorticity and Incompressible Flow, Cambridge University Press (2001) | MR
, ,[12] Dynamo action in magnetohydrodynamics and Hall magnetohydrodynamics, Astrophys. J. 587 (2003), 472 -481
, , ,[13] A review of magneto-vorticity induction in Hall-MHD plasmas, Plasma Phys. Control. Fusion 43 (2001), 195 -221
, ,[14] The Hall effect and the decay of magnetic fields, Astron. Astrophys. (1997), 685 -690
, ,[15] Tools for PDE. Pseudodifferential Operators, Paradifferential Operators and Layer Potentials, American Mathematical Society (2000) | MR | Zbl
,[16] Theory of Function Spaces I, Birkhäuser Basel (1983) | MR
,[17] Star formation and the Hall effect, Astrophys. Space Sci. 292 (2004), 317 -323
,Cited by Sources: