On the Cauchy problem of three‐dimensional compressible magneto‐micropolar fluids with vacuum

Mingyu Zhang

Mathematische Nachrichten, 2025, vol. 298, issue 5, 1449-1481

Abstract: In this paper, we study the Cauchy problem of three‐dimensional compressible magneto‐micropolar fluids. Applying the energy method and the structural characteristics of the model, the global existence and uniqueness of classical solutions are established provided that ∥B0∥L3+M0$\Vert \mathbf { B}_0\Vert _{L^3}+M_0$ is suitable small, where B0$\mathbf { B}_0$ and M0$M_0$ represent the initial magnetic field and upper bound of initial density. It is worth mentioning that both the vacuum states of initial density and the possible random largeness of initial energy are allowed. Thus, the results obtained particularly extend the one due to Wei et al., where the global well‐posedness of smooth solutions with small perturbations of initial data was proved.

Date: 2025
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