Abstract
In this paper, we derive the Liouville theorem of D-solutions to the stationary MHD system under the asymptotic assumption: one of the velocity field and the magnetic field approaches zero and the other approaches a non zero constant vector at infinity. Our result extends the corresponding one of D-solutions to the Navier–Stokes equations when the velocity approaches a non zero constant vector at infinity.
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Acknowledgements
Z. Li is supported by Natural Science Foundation of Jiangsu Province (No. BK20200803), National Natural Science Foundation of China (No. 12001285) and the Startup Foundation for Introducing Talent of NUIST (No. 2019r033). X. Pan is supported by Natural Science Foundation of Jiangsu Province (No. BK20180414) and National Natural Science Foundation of China (No. 11801268).
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Li, Z., Pan, X. Liouville theorem of the 3D stationary MHD system: for D-solutions converging to non-zero constant vectors. Nonlinear Differ. Equ. Appl. 28, 12 (2021). https://doi.org/10.1007/s00030-021-00674-y
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DOI: https://doi.org/10.1007/s00030-021-00674-y