Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity
The authors investigate the asymptotics of the solutions to the stationary Stokes and Navier-Stokes equations of a viscous incompressible fluid with additional flux conditions in a domain with paraboloidal outlets to infinity (an intermediate case between cylindrical and conical outlets). The complete asymptotic decomposition is constructed for the solution of the Stokes problem in the case when the right-hand side has either a compact support or a special series representation. For the solution of the nonlinear Navier-Stokes problem the asymptotic decomposition is constructed in the case of zero right-hand side. The obtained asymptotic decompositions are justified in weighted Hölder spaces.
scientific article; zbMATH DE number 1183131
scientific article