The weak solutions of Hopf type to 2D Maxwell flows with infinite number of relaxation times

The system of equations, describing motion of fluids of Maxwell type is considered
$$ \frac\partial{\partial t}v+v\cdot\nabla v-\int_0^t K(t-\tau)\Delta v(x,\tau)\,d\tau+\nabla p=f(x,t),\quad\operatorname{div}v=0. $$
Here $K(t)$ is exponential series $K(t)=\sum_{s=1}^\infty\beta_se ^{-\alpha_st}$. The existence of weak solution for initial boundary value problem
$$ v(x,0)=v_0(x),\quad v\cdot n|_{\partial\Omega}=0,\quad\operatorname{rot}v|_{\partial\Omega}=0 $$
is proved.