arXiv:2611.14662v1 Announce Type: new Abstract: We extend the differential structure on Wasserstein spaces of Schichl (arXiv:2508.15140) to the normed Wasserstein space $\mathbb{W}_1$ of finite signed measures, the natural setting for measure differential equations with source terms. We generalize the averaged flow dispersion and expectational flow operators to $\mathbb{W}_1$ and show that along divergence--free tangent vectors they act by measure--preserving flows, and further define source operators. As an application, we construct a purely Lagrangian splitting scheme for the incompressible Navier--Stokes equations on $\mathbb{R}^N$, inspired by the Averaged Flow Approximation Series (AFAS) in \cite{Schichl2025}. We recover, with explicit constants, the classical lifespan bound, a blow--up rate and the inviscid limit with rate $O(\eta^2)$, and a linearised scheme yields $L^{\infty}$, H\"older, $L^1$ and moment estimates for classical solutions.
Continue to arXiv Mathematics →You are being forwarded in 6s — stay on this page