Besse, Nicolas Lagrangian averaged gyrokinetic-waterbag continuum. (English) Zbl 1345.35114 Commun. Math. Sci. 14, No. 3, 593-626 (2016). 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. Reviewer: Eugene Postnikov (Kursk) 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 Keywords:Gyrokinetic-Waterbag model; gyrowaterbag model; well-posed problem; gyrokinetic turbulence; Lagrangian averaged models; Eulerian and Lagrangian variational principles; Gyrokinetic-Vlasov equations; multi-fluids systems; infinite-dimensional hyperbolic system of conservation laws in several space dimension; magnetically confined fusion plasmas Software:GMWB3D-SLC; CYLGYR; QUALIMUWABA PDFBibTeX XMLCite \textit{N. Besse}, Commun. Math. Sci. 14, No. 3, 593--626 (2016; Zbl 1345.35114) Full Text: DOI