The solvability of the second initial boundary-value problem for the linear, time-dependent system of Navier–Stokes equations

In a class of functions with Holder-continuous derivatives unique solvability is is proved for the problem of determining a solution of the linear, time-dependent system of Navier–Stokes equations with boundary data $\sum^3_{j=1}T_{ij}n_j$, $i=1,2,3$, where $n_j$ are the direction cosines of the exterior normal to the boundary and $T_{ij}$ are the components of the stress tensor.