Flow Representation of the Navier-Stokes Equations in Weighted Sobolev Spaces

Using Constantin-Iyer representation also known more generally as Euler-Lagrangian approach, we prove the local existence of the Navier-Stokes equations in weighted Sobolev spaces with external forcing on $\mathbf{R}^{d}$, for any dimension $d$ and $p$ such that $p>d\geq2$.