Euler and Navier-Stokes equations on the hyperbolic plane.
basic_science · Level V
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- Record sourced from PubMed, PMID 23091015.
- Also identified by DOI 10.1073/pnas.1210350109 and PMC identifier 3494927.
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Abstract
We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.