Energy conservation for the incompressible inhomogeneous Euler-Korteweg equations
Abstract
In this manuscript, we investigate the energy conservation for the incompressible inhomogeneous Euler-Korteweg equations in the whole space and the periodic domains when the density is away from the vacuum. We provide the two different proofs of the energy conservation of weak solutions. Compared with the previous results, the improvement here lies in the fact that $ \rho, u $ have weaker regularity in the temporal direction, which comes from the special techniques we adopted by eliminating the dependence on the time derivative of the velocity in the equation of the momentum.
Fields of Study & Subjects
Navier-Stokes equation solutions
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - B
- Volume
- 36
- Issue
- 0
- Pages
- 335–353
- Publication date
- 1 January 2026