Abstract
This paper concerns with a kind of chemotaxis-Stokes systems generalizing the prototype{nt+u⋅∇n=∇⋅(nm−1∇n)−∇⋅(n∇c)−nv,ct+u⋅∇c=Δc−c+v,vt+u⋅∇v=Δv−nv,ut=Δu+∇P+(n+v)∇Φ,∇⋅u=0 which characterizes the process of coral fertilization in ocean. By virtue of a novel approach on the basis of some conditional estimates for signal gradient and fluid velocity, it is proved that when m>1 an associated initial-boundary problem possesses a globally bounded weak solution in spatially three-dimensional setting, which extends the corresponding results obtained in [15]. Moreover, the obtained solutions stabilize to a certain constant equilibrium (n∞,v∞,v∞,0) with n∞:=1|Ω|{∫Ωn0−∫Ωv0}+ and v∞:=1|Ω|{∫Ωv0−∫Ωn0}+ as t→∞.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.