Lower bounds on the blowup rate of the axisymmetric NavierStokes equations
Lower bounds on the blowup rate of the axisymmetric NavierStokes equations

Robert Strain, Princeton University
Fine Hall 110
Consider axisymmetric strong solutions, v, of the incompressible NavierStokes equations in $\mathbb{R}^3$ with nontrivial swirl. Leray, in his 1934 Acta. Math paper, has shown that at a blowup time, $T$, such solutions would have to satisfy for some fixed $\epsilon_1>0$ $$ \liminf_{t\uparrow T} \sqrt{Tt} \sup_x v(x,t) \ge \epsilon_1$ $$ We will discuss our recent proof which rules out this scale invariant blowup rate: $$ v(x,t) \le C_*/\sqrt{Tt}. $$ Above $C_*$ is allowed to be large. This is joint work with Tsai, Chen and Yau.