Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain |
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Institution: | 1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, PR China;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;4. School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China |
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Abstract: | In this paper, we prove the energy conservation for the weak solutions of the three-dimensional ideal inhomogeneous magnetohydrodynamic (MHD) equations in a bounded domain. Two types of sufficient conditions on the regularity of the weak solutions are provided to ensure the energy conservation. Due to the presence of the boundary, we need to impose the boundedness in and the continuity in for the velocity and magnetic fields near the boundary. |
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Keywords: | Ideal inhomogeneous magnetohydrodynamic equations Weak solution Energy conservation |
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