2D Homogeneous Solutions to the Euler Equation

DOI10.1080/03605302.2015.1045073zbMath1329.35237arXiv1409.4322OpenAlexW1901372827MaRDI QIDQ3448246

Xue Luo, Roman Shvydkoy

Publication date: 23 October 2015

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4322

zbMATH Keywords

Euler equationself-similar solutionHamiltonian systemhomogeneous solutionOnsager conjecture

Mathematics Subject Classification ID

Related Items (12)

A proof of Onsager's conjecture ⋮ Energy conservation in two-dimensional incompressible ideal fluids ⋮ Non uniform rotating vortices and periodic orbits for the two-dimensional Euler equations ⋮ Intermittency and lower dimensional dissipation in incompressible fluids ⋮ Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II: Classification of axisymmetric no-swirl solutions ⋮ Uniformly rotating smooth solutions for the incompressible 2D Euler equations ⋮ Addendum: 2D homogeneous solutions to the Euler equation ⋮ The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view ⋮ Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations ⋮ Symmetry in stationary and uniformly rotating solutions of active scalar equations ⋮ Vanishing viscosity limit for homogeneous axisymmetric no-swirl solutions of stationary Navier-Stokes equations ⋮ Homogeneous solutions to the 3D Euler system

Cites Work

• Dissipative continuous Euler flows
• On formation of a locally self-similar collapse in the incompressible Euler equations
• The monotonicity of the period function for planar Hamiltonian vector fields
• Period function for a class of Hamiltonian systems
• Lectures on the Onsager conjecture
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