2015/09/28 by P. Stubbe, Peter Stubbe, Stubbe, Peter · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Conjecture #Dissipation #Energy (signal processing) #Euler equations #Euler's formula #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Kinetic energy #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Onsager reciprocal relations #Physics #Pure mathematics #Quantum mechanics #Statistical physics #Theoretical physics #Thermodynamics #Viscosity #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1509.08406
published in arXiv (Cornell University) (Cornell University)
arxiv created 2015/09/28 · openalex publication_date 2015/09/28 · arxiv updated 2015/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Onsager conjectured that solutions of the incompressible Euler equations possessing a certain degree of roughness do not conserve the kinetic energy. Since, within the physical frame of Onsager's conjecture, the kinetic energy is the only occurring energy, and thus identical with the total energy, the implication would be that the conservation of energy is not absolute, but subject to the properties of mathematical solutions. Further, Onsager introduced the concept of anomalous dissipation of kinetic energy without viscosity. Both these aspects are critically discussed and their shortcomings unveiled.