Model problems for n-dimensional generalized Stokes equations

We consider the Cauchy problem and the initial-boundary value problem for g eneralized Stokes equations with constant coefficients in the half-space {x (n) > 0}, n greater than or equal to 2. The solutions are constructed in th e form of sums of potentials for whose kernels pointwise estimates are give n. This makes it possible to obtain coercive estimates for solution of thes e problems in different norms. In the three-dimensional case this has been done in [1,2]. The result may be useful for the analysis of initial-boundar y value problem for equations of motion of non-newtonian fluids.