TY - JOUR
T1 - Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity
AU - Wang , Yuzhu
JO - Journal of Partial Differential Equations
VL - 1
SP - 1
EP - 13
PY - 2021
DA - 2021/01
SN - 34
DO - http://doi.org/10.4208/jpde.v34.n1.1
UR - https://global-sci.org/intro/article_detail/jpde/18551.html
KW - Hall-MHD system with mixed viscosity, global existence, smooth solutions.
AB - <p style="text-align: justify;">We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The
diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases
new difficulty in proving global smooth solutions. Moreover, Hall term heightens the
level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the
initial data is enough small.</p>