Mathematical Physics

    

A Mathematical Proof About Spatial Symmetry Invariance of Solution of the Three-Dimensional Navier-Stokes Equations

Authors: Shijun LIAO

We prove such a mathematical theorem that solution of the incompressible Navier-Stokes equations under periodic boundary condition has the same spatial symmetry for all t>0 as its smooth initial condition, if there exist the spatial symmetry for initial condition, the external force is steady-state, and the temporal Taylor series of velocity exists and has a non-zero radius of convergence for t >= 0. This theorem can be used to check the correctness and reliability of numerical simulation of Navier-Stokes equations for turbulent flows.

Comments: 5 Pages.

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[v1] 2026-03-16 00:46:43

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