| Abstract: |
| Chemotactic blow up in the context of the Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest singularity formation given that the fluid flow possesses mixing or diffusion enhancing properties and its amplitude is sufficiently strong - an effect that is conjectured to hold for more general classes of nonlinear PDE. In this talk, I will discuss some results on suppression of singularity formation in systems where Keller-Segel equation is coupled with fluid flow via buoyancy force. The talk is based on a joint work with Alexander Kiselev and Yao Yao. |
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