| Abstract: |
| we introduce both parabolic-elliptic Keller-Segel model and parabolic-parabolic Keller-Segel model in the background of a Couette flow with spatial variables in $R^3$. It is proved that for both parabolic-elliptic and parabolic-parabolic cases, a Couette flow with a suffciently large amplitude prevents the blow-up of solutions. This result is totally different from either the classical Keller-Segel model or the case with a large shear flow and the periodic spatial variable $x$; for those two cases, the solution may blow up. Here, we apply Green`s function method to capture the suppression of blow-up and prove the global existence of the solutions. |
|