Mathematical Analysis of the Navier-stokes Equations with Non Standard Boundary Conditions

One of the major applications of the Domain Decomposition TimeMarching Algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional ows. Another important application, is the coupling of a global Navier-Stokes problem with a local one in order to use di erent modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes systems with non standard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem. This work was supported by the National Aeronautics and Space Administration under NASA contract NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681-0001.