On the conservation of energy in two-dimensional incompressible flows

01/17/2020 ∙ by S. Lanthaler, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 21

page 25

page 28

page 29

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.