On the uniqueness of weak solutions of the 3D MHD equations in the Orlicz–Morrey space

Abstract

In this article, we show that if a Leray solution (u, b) to the 3D magneto-hydrodynamic equation belongs to with r ∈ (0, 1) and P > 1, then (u, b) is the unique Leray solution on (0, T).

Keywords:

• uniqueness
• weak solutions
• Orlicz–Morrey spaces

AMS Subject Classifications::

• 35Q35
• 35Q80
• 42B35
• 76N10

Acknowledgements

This work is partially supported by Grant-in-Aid for Young Scientists (B) No. 21740104, Japan Society for the Promotion of Science.