On the Cauchy problem for the stationary linear Navier-Stokes system (Q1375039)

Solutions to the generalized Cauchy problem for the linear stationary system of Navier-Stokes equations in a bounded 3-dimensional domain are to be determined by values of the velocity and the stress tensor given on a part of the boundary. The author constructs a Carleman matrix for this system and proves Theorem 1 (respectively, Theorem 2) that, given exact (respectively, approximate) values of the velocity and the stress tension, approximate solutions constructed with the help of the Carleman matrix converge to the exact solution of the problem. Analogous results are formulated for the case of domains of a cone-type.