Blow-up of smooth solutions to the isentropic compressible MHD equations

Abstract

This article studies the blow-up of smooth solutions to the isentropic compressible magnetohydrodynamic (MHD) equations (1.1(1) ) in , . We obtain that under physical conditions, if the initial density and magnetic have compact support, then any smooth radially symmetric solutions will blow up in finite time.

Keywords:

• compressible MHD equations
• isentropic fluids
• blow-up

AMS Subject Classifications:

• 35B44
• 76W05

Acknowledgments

The research was partially supported by the National Natural Science Foundation of China (No.11071057, No.11271052) and Tian Yuan Special Foundation ( No. 11226029). The authors would like to thank Prof. C. Miao and Prof. Q. Chen for their valuable discussions.