The geometry and analysis of the averaged Euler equations and a new diffeomorphism group

From MaRDI portal
Publication:1584725

DOI10.1007/PL00001631zbMath0979.58004arXivmath/9908103OpenAlexW2130006697MaRDI QIDQ1584725

Tudor S. Ratiu, Steve Shkoller, Jerrold E. Marsden

Publication date: 1 February 2002

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9908103



Related Items

Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics, Some remarks on a certain class of axisymmetric fluids of differential type, Uniform time of existence for the alpha Euler equations, Vortices on Closed Surfaces, The Hölder continuity of the solution map to the \(b\)-family equation in weak topology, The Lagrangian averaged Navier-Stokes equation with rough data in Sobolev spaces, \( H^m\) convergence of the second-grade fluid equations to Euler equations in \(\mathbb{R}^d\), Euler's fluid equations: Optimal control vs optimization, Non-conservative solutions of the Euler-\(\alpha\) equations, Strong convergence of the vorticity and conservation of the energy for the α-Euler equations, Central extensions of semidirect products and geodesic equations, A geometric look at momentum flux and stress in fluid mechanics, Structure-preserving model reduction for mechanical systems, Incompressible Euler equations with stochastic forcing: a geometric approach, The Limit $\alpha \to 0$ of the $\alpha$-Euler Equations in the Half-Plane with No-Slip Boundary Conditions and Vortex Sheet Initial Data, Stability criteria for the 2D \(\alpha\)-Euler equations, Uniform time of existence of the smooth solution for 3D Euler-α equations with periodic boundary conditions, Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics, Diffeomorphism groups of compact manifolds, THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID, Quantum kinematics of bosonic vortex loops, Geodesics on extensions of Lie groups and stability: The superconductivity equation, The Navier-Stokes-alpha model of fluid turbulence, Variational methods, multisymplectic geometry and continuum mechanics, Confinement of vorticity for the 2D Euler-\(\alpha\) equations, Vorticity dynamics and turbulence models for Large-Eddy Simulations, Global well-posedness for the averaged Euler equations in two dimensions, The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation, Global existence and uniqueness of solutions to the equations of second-grade fluids, Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems, Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers