Chaos in the incompressible Euler equation on manifolds of high dimension

DOI10.1007/s00222-021-01089-3zbMath1492.35210arXiv2104.00647OpenAlexW3147666566MaRDI QIDQ2131229

Francisco Torres de Lizaur

Publication date: 25 April 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.00647

zbMATH Keywords

Riemannian manifoldincompressible Euler equation

Mathematics Subject Classification ID

Attractors (35B41) Perturbations of ordinary differential equations (34D10) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37K99) Manifolds of mappings (58D15) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Methods of ordinary differential equations applied to PDEs (35A24) Euler equations (35Q31) PDEs on manifolds (35R01)

Related Items (9)

Looking at Euler flows through a contact mirror: universality and undecidability ⋮ Universality of Euler flows and flexibility of Reeb embeddings ⋮ Time quasi-periodic vortex patches of Euler equation in the plane ⋮ An h$h$‐principle for embeddings transverse to a contact structure ⋮ Geometric hydrodynamics in open problems ⋮ Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamics ⋮ Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher ⋮ Singularity formation in the incompressible Euler equation in finite and infinite time ⋮ Computability and Beltrami fields in Euclidean space

Cites Work

• Unnamed Item
• Unnamed Item
• KAM theory and the 3D Euler equation
• Knots and links in three-dimensional flows
• Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
• Structural stability of Lorenz attractors
• The structure of Lorenz attractors
• Wandering solutions of Euler's D-2 equation
• Topological transitivity of billiards in polygons
• Topological methods in hydrodynamics
• On the universality of the incompressible Euler equation on compact manifolds
• A steady Euler flow with compact support
• Multivariate simultaneous approximation
• On the sphere problem
• Global, local and dense non-mixing of the 3D Euler equation
• Existence of knotted vortex tubes in steady Euler flows
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Vorticity and Incompressible Flow
• Homogeneous solutions to the 3D Euler system
• Billiards in polygons and homogeneous foliations on C²
• Evolution of singularities, generalized Liapunov function and generalized integral for an ideal incompressible fluid
• SPLITTING OF THE SEPARATRICES AND THE NONEXISTENCE OF FIRST INTEGRALS IN SYSTEMS OF DIFFERENTIAL EQUATIONS OF HAMILTONIAN TYPE WITH TWO DEGREES OF FREEDOM
• A Geometric Approach to Regular Perturbation Theory with an Application to Hydrodynamics
• Quasi-periodic solutions of the 2D Euler equation
• On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows
• Invariant manifolds

This page was built for publication: Chaos in the incompressible Euler equation on manifolds of high dimension