Communications in Mathematical Sciences
Volume 19 (2021)
Global strong solutions for planar full compressible Hall-MHD equations with large initial data
Pages: 1913 – 1943
This paper establishes the global existence of strong solutions for planar compressible, viscous, heat-conductive (i.e., full fluids) Hall-MHD equations with large initial data. The uniform positive lower and upper bounds of the density are achieved by adopting the idea from [S. Jiang, Comm. Math. Phys. 200:181–193, 1999] for the Navier–Stokes equation and Calderón–Zygmund decomposition technique. Based on the bounds of the density and the skew-symmetric nature of the Hall term, we derive our conclusion of Theorem 1.1.
Hall-MHD, global strong solutions, large initial data
2010 Mathematics Subject Classification
35D35, 35Q35, 76W05
This work was partly supported by the National Science Foundation of China (Grant Nos. 11871407 and 12071390).
Received 16 January 2020
Accepted 7 April 2021
Published 7 September 2021