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<p>In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure, defining suitable energy functionals, and using a totally different iteration scheme, after the elaborate index analysis, we establish the global existence of strong solutions as long as the initial data is large enough. This is a big contrast to the classical results, where the initial data is a small perturbation of some resting states.</p>

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Global existence of large strong solutions to the 3D barotropic compressible Navier-Stokes equations with density-dependent viscosities

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Xiangdi Huang,
  • Jiaxu Li,
  • Rong Zhang

摘要

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure, defining suitable energy functionals, and using a totally different iteration scheme, after the elaborate index analysis, we establish the global existence of strong solutions as long as the initial data is large enough. This is a big contrast to the classical results, where the initial data is a small perturbation of some resting states.