On the blow-up criterion of magnetohydrodynamics equations in homogeneous Sobolev spaces

Abstract

In this paper, we obtain new lower bounds of the maximal solution of the magnetohydrodynamics equations in the homogeneous Sobolev space , for , when solutions blow-up in finite time. This gives us some new insight on the blow-up behavior of the solution.

Keywords:

• Magnethohydrodinamics equations
• blow-up criterion
• lower bounds

AMS Subject Classifications:

• 35Q40
• 35Q60
• 35Q61
• 76W05

Acknowledgements

We thank Prof. Paulo Zíngano for comments and fruitful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

D. Marcon was partially supported by CNPq – Brazil through the postdoctoral scholarship [PDJ/501839/2013-5].