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Local well-posedness of the EPDiff equation: a survey - MaRDI portal

Local well-posedness of the EPDiff equation: a survey (Q2397514)

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Language	Label	Description	Also known as
English	Local well-posedness of the EPDiff equation: a survey	scientific article

Statements

scholarly article

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Local well-posedness of the EPDiff equation: a survey (English)

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Journal of Geometric Mechanics

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publication date

22 May 2017

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full work available at URL

https://arxiv.org/abs/1611.05034

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zbMATH Keywords

EPDiff equation

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diffeomorphism groups

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Sobolev metrics of fractional order

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MaRDI profile type

MaRDI publication profile

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Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits

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Topological methods in hydrodynamics

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The various definitions of the derivative in linear topological spaces

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Local and global well-posedness of the fractional order EPDiff equation on \(\mathbb{R}^d\)

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Geometric investigations of a vorticity model equation

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The Least Action Principle and the Related Concept of Generalized Flows for Incompressible Perfect Fluids

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Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations

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An integrable shallow water equation with peaked solitons

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Euler-Poincaré-Arnold equations on semi-direct products. II

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On geodesic exponential maps of the Virasoro group

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Geodesic flow on the diffeomorphism group of the circle

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On the geometry of the diffeomorphism group of the circle

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A simple one‐dimensional model for the three‐dimensional vorticity equation

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Groups of diffeomorphisms and the motion of an incompressible fluid

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On the space of Riemannian metrics

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A Concise Presentation of the Euler Equations of Hydrodynamics

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Geometry of manifolds of maps

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The Degasperis-Procesi equation as a non-metric Euler equation

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Geodesic completeness for Sobolev \(H^{s}\)-metrics on the diffeomorphism group of the circle

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Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle

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The geometry of a vorticity model equation

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The inverse function theorem of Nash and Moser

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Existence of the Riemannian exponential mapping of a diffeomorphism group applied with a Sobolev metric

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On the regularity of the composition of diffeomorphisms

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Commutator estimates and the euler and navier-stokes equations

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Differential calculus in locally convex spaces

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Euler equations on homogeneous spaces and Virasoro orbits

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The Camassa–Holm equation as a geodesic flow on the diffeomorphism group

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The Hunter-Saxton equation describes the geodesic flow on a sphere

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The Hunter–Saxton Equation: A Geometric Approach

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Integrable evolution equations on spaces of tensor densities and their peakon solutions

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Vorticity and Incompressible Flow

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Well-posedness of modified Camassa-Holm equations

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On Euler's equation and `EPDiff'

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A shallow water equation as a geodesic flow on the Bott-Virasoro group

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Classical solutions of the periodic Camassa-Holm equation.

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Fredholm properties of Riemannian exponential maps on diffeomorphism groups

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Pseudo-Differential Operators and Symmetries

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Geometry and curvature of diffeomorphism groups with \(H^1\) metric and mean hydrodynamics

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Analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid.

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Generalized fluid flows, their approximation and applications

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ON THE GEOMETRY OF THE GROUP OF DIFFEOMORPHISMS AND THE DYNAMICS OF AN IDEAL INCOMPRESSIBLE FLUID

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Local Geometry of Deformable Templates

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On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric

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Identifiers

zbMATH Open document ID

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10.3934/jgm.2017007

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2397514

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