Dissipative Energy Estimates for Non-Autonomous Stoke Equation

This paper derives the weighted energy equality for the linear nonautonomous stokes problem. This is a part of the process of solving Navier-Stokes equations to exclude the pressure term before it is determined in which function space solution (u,p) lies. A correction term vφ is introduced when the pressure term is excluded in the Navier-Stokes system and the energy estimate is computed; because the parameter vφ is only an artificial creation meant to exclude the pressure, thereby gauge the impact of the parameter on the final estimates. It is discovered that the introduction of a correction parameter vφ did not essentially change the estimates as it is only found to be − small. Hence, the energy estimate for the Navier-Stokes system remains valid.