Well-posedness and attractors of the multi-dimensional hyperviscous magnetohydrodynamic equations

Abstract

The multi-dimensional hyperviscous magnetohydrodynamic equations are considered in this paper. The well-posedness of the multi-dimensional hyperviscous magnetohydrodynamic equations is proved. Global attractor of the multi-dimensional hyperviscous magnetohydrodynamic equations is proved in $H^{\frac{1}{2}+\frac{n}{4}}\times H^{\frac{1}{2}+\frac{n}{4}}$ and $H^{1+\frac{n}{2}}\times H^{1+\frac{n}{2}}$.

Keywords:

• Magnetohydrodynamic equations
• strong solution
• global attractor

2010 Mathematics Subject Classifications:

• 35B41
• 35D35
• 76W05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by the National Natural Science Foundation of China No. 11901342,11701269,11901302 and China Postdoctoral Science Foundation No. 2019M652350, Postdoctoral Innovation Project of Shandong Province No. 202003040, the Natural Science Foundation of Shandong Province No. ZR2018QA002.