- Journal Article
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier–Stokes equations and a Monte Carlo-spectral viscosity numerical approximation, respectively. We characterize this conservation of energy in terms of a uniform decay of the so-called structure function, allowing us to extend existing results on energy conservation. Moreover, we present numerical experiments with a wide variety of initial data to validate our theory and to observe energy conservation in a large class of two-dimensional incompressible flows. © 2021 IOP Publishing Ltd & London Mathematical Society Show more
Journal / seriesNonlinearity
Pages / Article No.
PublisherInstitute of Physics
SubjectIncompressible flow; Incompressible Euler equations; Anomalous dissipation; Turbulence; Structure function; Statistical solution; Energy conservation
Organisational unit03851 - Mishra, Siddhartha / Mishra, Siddhartha
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