Abstract
In this paper, we consider the Cauchy problem of a full compressible Hall-MHD system. $$\displaystyle \dot{H}^{-s}\ \ \left( 0<s\le \frac{3}{2}\right) $$ Sobolev norms are shown to be preserved along time evolution. Boundedness and time decay of the higher-order spatial derivatives of the smooth solutions are given.
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