Abstract
In this paper, we consider the large time behavior of solutions to the three-dimensional compressible Hall-magneto-hydrodynamics equations. We first establish the uniform estimates of the global smooth solution with respect to the Hall coefficient \({\epsilon}\). Then we obtain the optimal decay estimates with the aid of a negative Sobolev space. We next show that the unique smooth solution of the compressible Hall-magneto-hydrodynamics system converges globally in time to the smooth solution of the compressible magneto-hydrodynamics system as \({\epsilon}\) tends to zero. We also give the convergence rate estimates for any given positive time.
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Xiang, Z. On the Cauchy problem for the compressible Hall-magneto-hydrodynamics equations. J. Evol. Equ. 17, 685–715 (2017). https://doi.org/10.1007/s00028-016-0333-7
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DOI: https://doi.org/10.1007/s00028-016-0333-7