On 2D Euler equations. I. On the energy–Casimir stabilities and the spectra for linearized 2D Euler equations
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Publication:2737848
DOI10.1063/1.533176zbMath0997.37044arXivmath/0010240OpenAlexW2077143683MaRDI QIDQ2737848
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0010240
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Incompressible inviscid fluids (76B99)
Related Items (16)
CHAOS IN WAVE INTERACTIONS ⋮ Applications of Nambu mechanics to systems of hydrodynamical type ⋮ Instability of unidirectional flows for the 2D Navier-Stokes equations and related \(\alpha\)-models ⋮ Instability of unidirectional flows for the 2D \(\alpha\)-Euler equations ⋮ Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity ⋮ An Evans function for the linearised 2D Euler equations using Hill's determinant ⋮ Nonlinear stability of sinusoidal Euler flows on a flat two-torus ⋮ Instability of Equilibria for the Two-Dimensional Euler Equations on the Torus ⋮ On the dynamics of Navier-Stokes and Euler equations ⋮ Enstrophy dissipation in freely evolving two-dimensional turbulence ⋮ A Lax pair for the two dimensional Euler equation ⋮ Applications of Nambu Mechanics to Systems of Hydrodynamical Type II ⋮ Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor ⋮ Stability results for idealized shear flows on a rectangular periodic domain ⋮ Stability Theory of the 3-Dimensional Euler Equations ⋮ Stability of Rossby waves in the \(\beta\)-plane approximation
Cites Work
- Decaying, two-dimensional, Navier-Stokes turbulence at very long times
- Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
- Nonlinear stability of fluid and plasma equilibria
- Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid
- Statistical equilibrium states for two-dimensional flows
- On an apriori estimate in the theory of hydrodynamical stability
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