Conservation of energy for the Euler-Korteweg equations

TL;DR

This paper investigates the energy conservation principle for the Euler-Korteweg system, establishing a regularity condition under which weak solutions conserve total energy, with applications to Quantum Hydrodynamics.

Contribution

It introduces an Onsager-type regularity criterion ensuring energy conservation for weak solutions of the Euler-Korteweg system, including quantum hydrodynamics.

Findings

Established a regularity condition for energy conservation.

Applied the criterion to Quantum Hydrodynamics.

Enhanced understanding of weak solution behavior.

Abstract

In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.