@article{Gao2023, 
author = {Kai Gao},
title = {Global boundedness of classical solutions to a Keller-Segel-Navier-Stokes system involving saturated sensitivity and indirect signal production in two dimensions},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {3},
pages = {1710-1736},
keywords = {Keller-Segel-Navier-Stokes system, tensor-valued sensitivity, indirect signal production, classical solution, global boundedness},
url = {https://www.sciopen.com/article/10.3934/era.2023089},
doi = {10.3934/era.2023089},
abstract = {This paper is concerned with the following Keller–Segel–Navier–Stokes system with indirect signal production and tensor-valued sensitivity:          {                                        n                          t                                +          u          ⋅          ∇          n          =          Δ          n          −          ∇          ⋅          (          n          S          (          x          ,          n          ,          v          ,          w          )          ∇          v          )          ,                                    x          ∈          Ω          ,          t          >          0          ,                                                  v                          t                                +          u          ⋅          ∇          v          =          Δ          v          −          v          +          w          ,                                    x          ∈          Ω          ,          t          >          0          ,                                                  w                          t                                +          u          ⋅          ∇          w          =          Δ          w          −          w          +          n          ,                                    x          ∈          Ω          ,          t          >          0          ,                                                  u                          t                                +          κ          (          u          ⋅          ∇          )          u          +          ∇          P          =          Δ          u          +          n          ∇          ϕ          ,                                    x          ∈          Ω          ,          t          >          0          ,                                      ∇          ⋅          u          =          0          ,                                    x          ∈          Ω          ,          t          >          0          ,                                                                                                                  (      ♡    )in a bounded domain    Ω  ⊂            R        2   with smooth boundary, where    κ  ∈      R  ,    ϕ  ∈      W          2      ,      ∞        (  Ω  ), and    S is a given function with values in              R              2      ×      2       which satisfies        |    S  (  x  ,  v  ,  w  ,  u  )      |    ≤      C          S        (  n  +  1      )          −      α       with        C          S        >  0. If    α  >  0, then for any sufficiently smooth initial data, there exists a globally classical solution which is bounded for the corresponding initial-boundary value problem of system (♡).}
}