Local well-posedness to the three-dimensional barotropic compressible magnetohydrodynamic equations with vacuum

This paper considers the local well-posedness of strong solutions to the three-dimensional barotropic compressible magnetohydrodynamic equations with the initial density containing vacuum. We first derive the local existence and uniqueness of strong solutions. Then, we show the continuous dependence of strong solutions on the initial data under an additional compatibility condition.

Automated summary

This paper discusses the local well-posedness of strong solutions to the three-dimensional barotropic compressible magnetohydrodynamic equations with initial density containing vacuum. The authors first establish the local existence and uniqueness of strong solutions, and then demonstrate the continuous dependence of strong solutions on the initial data under an additional compatibility condition.