Existence and Uniqueness Proof for the Transport Equation and the Orthogonal Dynamics Equation for Zwanzig's Projection on Gaussian Spaces: A Vanishing Viscosity Method

Christoph Widder

We prove the existence of unique solutions $u\in H^1(0,T;L_{\gamma }^2({\mathbb{R}}^n))\cap L^2(0,T;H_{\gamma }^1({\mathbb{R}}^n))$ of the transport equation $u_t=F\cdot \nabla u+f$ and the orthogona…