Recently solutions to the aggregation equation on compact Riemannian Manifolds have been studied with different techniques. This work demonstrates the small time existence of measure-valued solutions for suitably regular intrinsic potentials. The main tool is the use of the minimizing movement scheme which together with the optimality conditions yield a finite speed of propagation. The main technical difficulty is non-differentiability of the potential in the cut locus which is resolved via the propagation properties of geodesic interpolations of the minimizing movement scheme and passes to the limit as the time step goes to zero.
Borel summability of Navier-Stokes equation in $\mathbb{R}^3$ and small time existence
A note on Kazdan-Warner type equations on compact Riemannian manifolds
A global scheme for the incompressible Navier-Stokes equation on compact Riemannian manifolds
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