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.
@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}, volume = {31}, year = {2014}, pages = {555-565}, doi = {10.1016/j.anihpc.2013.04.006}, mrnumber = {3208454}, zbl = {1297.35064}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 31 (2014) pp. 555-565. doi : 10.1016/j.anihpc.2013.04.006. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_3_555_0/
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