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Local existence of compressible MHD equations without initial compatibility conditions
  • Yiying Zhang,
  • Zhenhua Guo,
  • Li Fang
Yiying Zhang
Northwest University School of Mathematics
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Zhenhua Guo
Guangxi University School of Mathematics and Information Science
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Li Fang
Northwest University School of Mathematics

Corresponding Author:[email protected]

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Abstract

In this paper, we study the initial-boundary value problem of three-dimensional viscous, compressible, and heat conductive magnetohydrodynamic equations. Local existence and uniqueness of strong solutions is established with any such initial data that the initial compatibility conditions do not be required. The analysis is based on some suitable prior estimates for the strong coupling term u·∇ H and strong nonlinear term curl H × H . Our proof of the existence and uniqueness of solutions is in the Lagrangian coordinates first and then transformed back to the Euler coordinates.
08 Mar 2024Review(s) Completed, Editorial Evaluation Pending
14 Mar 20241st Revision Received
14 Mar 2024Submission Checks Completed
14 Mar 2024Assigned to Editor
14 Mar 2024Review(s) Completed, Editorial Evaluation Pending
15 Mar 2024Reviewer(s) Assigned