Abstract
AbstractThis paper is concerned with the effects of nonlinear sensitivity on boundedness of solutions for the following chemotaxis‐Stokes system in a smoothly bounded domain under no‐flux boundary conditions for and no‐slip boundary conditions for u, where n and m denote the densities of unfertilized sperms and eggs, respectively, c stands for the concentration of the signal, u represents the velocity of fluid, P is the pressure within the fluid and ϕ is the gravitational potential. This system describes the process of coral fertilization occurring in ocean flow. Based on the novel conditional estimates for c and u, it is proved that for all appropriately regular nonnegative initial data, this system possesses a unique globally bounded solution provided that satisfies with , which improves the known subcritical exponent under fluid‐free case.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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