Instantaneous blowup of incompressible flow with passive tracer

Mimi Dai, Xiaotong "Dawson" Yang

We construct a family of solutions $(u,b)$ of the incompressible flow with a passive tracer for which both $\Vert u(t){\Vert }_{L^{\infty }}$ and $\Vert b(t){\Vert }_{L^{\infty }}$ blow up at time $T_{\ast }$. Aw…