Initial-boundary value problem with a free surface condition for the modified Navier–Stokes equations

In this paper we study the global classical solvability on the semiaxis $t\in\mathbb R^+$ of the second initial-boundary value problem with a free surface condition (0.1) for other modified Navier–Stokes equations: Ladyzhenskaya's equations (0.3), equations of Jeffrey–Oldroyd fluids (0.4), equations of Kelvin–Voight fluids (0.5) and equations of aqueous solutions of polymers (0.6). Bibliography: 31 titles.