Weak martingale solution of stochastic critical Oldroyd-B type models perturbed by pure jump noise

We investigate the existence of a weak martingale solution for a
two-dimensional critical viscoelastic flow of the Oldroyd type driven
by pure jump Levy noise. Due to the viscoelastic nature, noise in the
equation modeling stress tensor is considered in the Marcus canonical
form. Owing to the lack of dissipation and taking into account
of the structure of the non-linear terms, the proof requires higher
order estimates