Orlandi and Carnevale [37] argue that the nonlinear amplification of vorticity in inviscid interaction is a candidate for the appearance of a finite-time singularity of the second kind starting from smooth initial data, check Eq. (3.15) in Chap. 3 for definition. The ode

\[ \frac{\partial \Phi}{\partial t}=\Phi^{2} \]

with initial condition \(\Phi(0)>0\) is a simplified version of the vorticity pde. It has a finite-time singularity developing from positive initial data. Prove this.

Eq. (3.15)

Transcribed Image Text:

0 T dt'||||L(D)(t) <