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

TL;DR

This paper introduces a new time-discrete scheme for solving Navier-Stokes equations inspired by material differentiation and discrete Morse semi-flow, aiming to enhance the analytical tools for these systems.

Contribution

The paper proposes a novel scheme combining material differentiation with discrete Morse semi-flow for Navier-Stokes systems, offering a new approach to their analysis.

Findings

The scheme satisfies the first energy inequality under certain assumptions.

It does not produce new results but provides a foundation for further development.

Potential for more sophisticated schemes to advance Navier-Stokes studies.

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.