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<p>In this paper, we study the initial boundary value problem for the three-dimensional (3D) nonhomogeneous incompressible micropolar fluid equations. We establish the global well-posedness of the system under lower regularity assumptions on the initial data. Compared with the previous results, our work allows for the presence of initial vacuum and discontinuous initial density, and no additional compatibility conditions are imposed on the initial data. As a by-product, we also establish the exponential decay in time of the solution by virtue of some a priori time-weighted estimates.</p>

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Global well-posedness and decay of the solutions for 3D nonhomogeneous incompressible micropolar fluid equations with rough initial density and vacuum

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Shengquan Liu,
  • Hexue Zhang

摘要

In this paper, we study the initial boundary value problem for the three-dimensional (3D) nonhomogeneous incompressible micropolar fluid equations. We establish the global well-posedness of the system under lower regularity assumptions on the initial data. Compared with the previous results, our work allows for the presence of initial vacuum and discontinuous initial density, and no additional compatibility conditions are imposed on the initial data. As a by-product, we also establish the exponential decay in time of the solution by virtue of some a priori time-weighted estimates.