Following the lines of Chapter 11, we can apply the results of Section 5.1 to study mechanical systems on the configuration spaces \(\mathcal{D}^{s}(M)\) , H s (M,M), or H s (M,N) with kinetic energy given by the (weak) Riemannian metric. Here we analyze those systems which are naturally related to certain problems of hydrodynamics. Note that according to the Lagrangian formalism, a trajectory of such a system gives the flow of a fluid.


External Force Euler Equation Burger Equation Integral Manifold Regularity Theorem 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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