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Lagrangian averaged gyrokinetic-waterbag continuum. (English) Zbl 1345.35114

The considered Lagrangian averaged gyrowaterbag continuum has definite advantages over another approaches to description of turbulent motions since it operates with natural and uniform mathematical structures, which are the same for the whole cascade of scales and is naturally connected with the hyperbolic conservation laws. The principal idea of this work consists of the construction of an averaged action for a set of spatial scales supplied with the consequent application of a least-action principle to derive equations of motion. The main theorem proven affirms well-posedness of the derived equations, and, correspondingly, existence and uniqueness of their classical solutions.

MSC:

35Q83 Vlasov equations
35F55 Initial value problems for systems of nonlinear first-order PDEs
35L65 Hyperbolic conservation laws
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76F02 Fundamentals of turbulence
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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