GEOMETRY OF L²(Ω, g)

Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space $L^2({\Omega},\;g)$, which is the weighted space of $L^2({\Omega})$, as natural generalized space of $L^2({\Omega})$ which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space $L^2({\Omega},\;g)$ as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on $L^2_{per}({\Omega},\;g)$) and compare with the one on $L^2_{per}({\Omega})$.