Suppression of blow-up in a fourth-order parabolic model via Couette flow in whole space
アブストラクト
In this talk, I will discuss the global existence and large-time behavior of solutions to a fourth-order parabolic equation with Couette flow. Using Green's function method, I will describe enhanced dissipation through a refined space-time structure, and thereby establish both global existence and decay estimates for the solutions. The main results demonstrate that the blow-up phenomenon of solutions can be suppressed by the enhanced dissipation associated with large Couette flows.