Abstract
This paper deals with the self‐consistent chemotaxis–Navier–Stokes system with porous medium diffusion in the two‐dimensional smoothly bounded domain, where the gravitational potential is given function. Systems of this type involve the effect of gravity on cells ( ) and the effect of the chemotactic force on fluid ( ), which leads to a stronger coupling than usual chemotaxis‐fluid system that proposed by Tuval et al. (Proc. Nat. Acad. Sci. 102 (2005), 2277‐2282) and studied widely in the most existing literatures. Under no‐flux boundary conditions for and and no‐slip boundary condition for , it is proved that the system admits at least one global weak solution which is uniformly bounded if . In particular, our result improves that established by Wang (Discr. Cont. Dyn. Syst. S 13 (2020), 329‐349), which asserts the global existence of weak solutions under the constraint .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
