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<p>In this paper, we investigate the global existence and boundedness of solutions to a two-dimensional chemotaxis-(Navier-)Stokes model which describes the process of coral fertilization occurring in ocean flow in bounded domain, where the interplay among Laplacian diffusion, chemotaxis cross diffusion and the fluid dynamic mechanism have been considered. It is proved that if the indexes satisfy some conditions, then for any reasonably smooth initial data, the corresponding Neumann-Neumann-Neumann-Dirichlet problem possesses a global classical solution. Moreover, the corresponding initial-boundary problem admits a unique global classical solution which is uniformly bounded on Ω × (0, ∞) under some stronger assumptions.</p>

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Some Further Progress for Existence and Boundedness of Solutions to a Two-dimensional Chemotaxis-(Navier-) Stokes System Modeling Coral Fertilization

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Jia-shan Zheng,
  • Kai-qiang Li

摘要

In this paper, we investigate the global existence and boundedness of solutions to a two-dimensional chemotaxis-(Navier-)Stokes model which describes the process of coral fertilization occurring in ocean flow in bounded domain, where the interplay among Laplacian diffusion, chemotaxis cross diffusion and the fluid dynamic mechanism have been considered. It is proved that if the indexes satisfy some conditions, then for any reasonably smooth initial data, the corresponding Neumann-Neumann-Neumann-Dirichlet problem possesses a global classical solution. Moreover, the corresponding initial-boundary problem admits a unique global classical solution which is uniformly bounded on Ω × (0, ∞) under some stronger assumptions.