A microlocal lift of Navier-Stokes dynamics on manifolds yields an if-and-only-if geometric criterion for solution blow-up in terms of deformation integrability, directional entropy, and lifted energy.
Gromov,A topological technique for the construc- tion of solutions of differential equations and inequalities
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On Geometric Evolution and Microlocal Regularity of the Navier-Stokes Equations
A microlocal lift of Navier-Stokes dynamics on manifolds yields an if-and-only-if geometric criterion for solution blow-up in terms of deformation integrability, directional entropy, and lifted energy.