Eulerian and Lagrangian stability in Zeitlin's model of hydrodynamics

Hydrodynamic stability (76E99) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Cites Work

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Euler equation on a rotating surface
Nonpositive curvature on the area-preserving diffeomorphism group
Semigroups of linear operators and applications to partial differential equations
Curvature of groups of diffeomorphisms preserving the measure of the 2- sphere
Some properties of matrix harmonics on \(S^2\)
Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
Mathematical analysis of a structure-preserving approximation of the bidimensional vorticity equation
For ideal fluids, Eulerian and Lagrangian instabilities are equivalent
\(gl(\infty{})\) and geometric quantization
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Curvatures of Sobolev metrics on diffeomorphism groups
Structure of the curvature tensor of the group of measure-preserving diffeomorphisms of a compact two-dimensional manifold
Area-preserving diffeomorphisms and the stability of the atmosphere
DIFFEOMORPHISM GROUPS, QUANTIZATION, AND SU(∞)
Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid
Sharp correspondence principle and quantum measurements
Canonical scale separation in two-dimensional incompressible hydrodynamics
A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics
Statistically relevant conserved quantities for truncated quasigeostrophic flow
Symbol Correspondences for Spin Systems