Local well-posedness of strong solutions for the nonhomogeneous MHD equations with a slip boundary conditions. (English) Zbl 1499.35506
Summary: This article is concerned with the 3D nonhomogeneous incompressible magneto- hydrodynamics equations with a slip boundary conditions in bounded domain. We obtain weighted estimates of the velocity and magnetic field, and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
Keywords:
nonhomogeneous MHD equations; local existence and uniqueness; vacuum; \(t\)-weighted \(H_2\) estimate; Galerkin approximationReferences:
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