A Nash-Moser approach for the Euler-Arnold equations

DOI10.1007/s00605-019-01344-zzbMath1440.35264OpenAlexW2980515669MaRDI QIDQ2187958

Nicolae Lupa, Emanuel-Ciprian Cismas

Publication date: 3 June 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-019-01344-z

zbMATH Keywords

Euler equationsNash-Moser theoremelliptic pseudo-differential operators

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with fluid mechanics (35Q35) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Graded Fréchet spaces and tame operators (46A61)

Cites Work

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• Euler-Poincaré equations on semi-direct products
• Euler-Poincaré-Arnold equations on semi-direct products. II
• The imbedding problem for Riemannian manifolds
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Partial differential equations. III: Nonlinear equations.
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Local and global well-posedness of the fractional order EPDiff equation on \(\mathbb{R}^d\)
• Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Fredholm properties of Riemannian exponential maps on diffeomorphism groups
• Non-Uniform Dependence for the Periodic CH Equation
• Pseudo-Differential Operators and Symmetries
• An Inverse Function Theorem for Fréchet Spaces Satisfying a Smoothing Property and (DN)
• The inverse function theorem of Nash and Moser
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• On the evolution of sharp fronts for the quasi‐geostrophic equation
• Geometrical Methods for Equations of Hydrodynamical Type
• The Cauchy problem for the Novikov equation