Onsager’s energy conservation of solutions for density-dependent Euler equations in [formula omitted

Abstract

This article is devoted to the study of energy conservation of weak solutions for the incompressible inhomogeneous Euler equations in Td, d>1. We give two sufficient conditions to prove the energy conservation, which only include a regularity of space (and time) on the velocity u. This is different from these results in Chen (2020), Chen and Yu (2019) and Nguyen et al. (2020), which contain the regularity of ∂tρ and the pressure p. In particular, our assumption in theorems is weaker than the assumption of Theorem 1.2 in Chen (2020) and the assumption of regularity of density of Theorem 1.1 in Chen and Yu (2019).