Some nonstationary linear and quasilinear systems occurring in the investigation of the motion of viscous fluids

We prove existence theorems for the solutions of initial- and boundary-value problems for different linear and quasilinear systems of third-order equations which generalize the Navier–Stokes equations and which are model equations for the description of the flow of well-determined classes of non-Newtonian fluids possessing relaxational properties. We also prove existence theorems and stability theorems on an arbitrary finite time interval of the solutions of initial-and boundary-value (IBV) problems for the alternative model of the Korteweg–de Vries equation.