Euler and Navier-Stokes equations on the hyperbolic plane.
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 109 45 شماره
صفحات -
تاریخ انتشار 2012