### Electronic Research Archive

2021, Issue 1: 1783-1801. doi: 10.3934/era.2020091

# Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations

• Received: 01 January 2020 Revised: 01 June 2020 Published: 16 September 2020
• Primary: 35Q30, 35Q35, 76E25, 76D03

• We prove some results on the stability of slow stationary solutions of the MHD equations in two- and three-dimensional bounded domains for external force fields that are asymptotically autonomous. Our results show that weak solutions are asymptotically stable in time in the $L^2$-norm. Further, assuming certain regularity hypotheses on the problem data, strong solutions are asymptotically stable in the $H^1$ and $H^2$-norms.

Citation: José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations[J]. Electronic Research Archive, 2021, 29(1): 1783-1801. doi: 10.3934/era.2020091

### Related Papers:

• We prove some results on the stability of slow stationary solutions of the MHD equations in two- and three-dimensional bounded domains for external force fields that are asymptotically autonomous. Our results show that weak solutions are asymptotically stable in time in the $L^2$-norm. Further, assuming certain regularity hypotheses on the problem data, strong solutions are asymptotically stable in the $H^1$ and $H^2$-norms.

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