On a time-discrete approach to solving Navier-Stokes systems

Abstract: We present a new scheme for solving Navier-Stokes systems. This is inspired by material differentiation and combined with discrete Morse semi-flow. The solution has the first energy inequality, we set some assumption though. This result crucially does not provide any new result, but I believe that by making my scheme is more sophisticated, we can develop the study of Navier-Stokes systems.