An error estimate uniform in time for spectral Galerkln approximations of the Kelvin-Voight problem

An error estimate uniform in time for spectral Galerkin approximations for solutions of initial boundary-value problem for the equations of motion of Kelvin–Voight fluids (1), (2):
$$ \sup_{t\geqslant0}||v_x-v_x^N||_{2,\Omega_t}\leqslant c\lambda_{N+1}^{-1/2} $$
is received; we suppose that solution $v$ is conditionally exponentially stable.