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Construction of weak solutions of the Navier-Stokes equations on Riemannian manifold by minimizing variational functionals. (English) Zbl 0944.58021
The author considers the nonstationary equations on Riemannian manifolds. By the method of the discrete Morse semi-flows, the author first constructs an approximate solution, then proves the stability of this scheme and obtains the global weak solutions of Leray-Hopf type even if the spectrum bottom is zero.
Reviewer: Weike Wang (Wuhan)

MSC:
58J45 Hyperbolic equations on manifolds
35L65 Hyperbolic conservation laws
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