We consider a system coupling the parabolic-parabolic chemotaxis equations to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criterions. For two dimensional chemotaxis-Navier-Stokes equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observations in  on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with stronger restriction on the consumption rate and chemotactic sensitivity.
|Number of pages||27|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 2013 Jun|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics