论文信息 - Euler and Navier–Stokes equations on the hyperbolic plane

Euler and Navier–Stokes equations on the hyperbolic plane

We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍn whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

Boris Khesin | Gerard Misiolek

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