学术报告（王维克 2025.4.21）

摘要：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 sufficiently 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.