First boundary value problem for the equations of hydrodynamics in a domain with a piecewise-smooth boundary

One considers the first boundary value problem for the Stokes and Navier-Stokes equations in a bounded domain with a piecewise-smooth boundary without zero angles. In Theorems 1 and 2 one gives solvability conditions in certain weighted spaces of Sobolev or Hölder type. Pointwise estimates for the Green tensor are formulated. Theorem 3 represents a generalization of the Miranda-Agmon maximum principle, while in Theorem 4 one gives conditions under which one has an estimate in W²₂ ().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematlcheskogo Instituta im. V. A. Steklova Akad Nauk SSSR, Vol. 96, pp. 179–186, 1980.