Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
Published 2017-07-31Version 1
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states regularity requirements for weak solutions of the incompressible Euler system to conserve energy. Further we survey results providing optimal sufficient regularity conditions for energy conservation for other balance laws: compressible Euler, Navier-Stokes, magnetohydrodynamics and general conservation laws.
A new proof to the energy conservation for the Navier-Stokes equations
On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system
Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions
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