On strong solutions to the compressible Hall-magnetohydrodynamic system |
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| Affiliation: | 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. Department of Mathematics, Inha University, Incheon 402-751, Republic of Korea;5. School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China;1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, 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;1. Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, PR China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China;1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China;2. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;1. School of Mathematics and Statistics, Nanyang Normal University, Henan 473061, PR China;2. School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China |
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| Abstract: | In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established. |
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| Keywords: | Hall-MHD Compressible Strong solutions Decay |
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