Onsager’s Conjecture for the Incompressible Euler Equations in Bounded Domains

2017/07/11 by Claude Bardos, Edriss S. Titi · 1 citation
Mathematics · Physics and Astronomy · #Boundary (topology) #Bounded function #Compressibility #Conjecture #Constant (computer programming) #Domain (mathematical analysis) #Euler equations #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Semi-implicit Euler method #Vector field #math.AP #msc:35Q31 #physics.flu-dyn

paper · pdf · doi:10.1007/s00205-017-1189-x

arxiv created 2017/07/11 · openalex created_date 2017/07/21 · openalex publication_date 2017/11/02 · arxiv updated 2017/12/06 · openalex updated_date 2026/08/05

Abstract

The goal of this note is to show that, also in a bounded domain Ω⊂ ℝⁿ, with ∂ Ω∈ C², any weak solution, (u(x,t),p(x,t)), of the Euler equations of ideal incompressible fluid in Ω× (0,T) ⊂ ℝⁿ×ℝ_t, with the impermeability boundary condition: u⋅ n =0 on ∂Ω×(0,T), is of constant energy on the interval (0,T) provided the velocity field u ∈ L³((0,T); C^0,α(Ω)), with α>\frac13 .

Citations

• Energy conservation for the weak solutions of the compressible Navier-Stokes equations
• Statistical hydrodynamics

Cited by

• Beyond chaos: fluctuations, anomalies and spontaneous stochasticity in fluid turbulence