The Asymptotic Limit of the Navier–Stokes–Poisson–Korteweg Equations

This paper considers the asymptotic problem for the Navier–Stokes–Poisson–Korteweg system with density‐dependent viscosity and cold pressure on the three‐dimensional torus , focusing on the incompressible limit and the vanishing capillarity limit. The convergence of the velocity field is examined via the action of the Leray operator, and the nonlinear terms are analyzed through the harmonic oscillator operator to show convergence in the distributional sense to gradient terms. Finally, we prove that the system converges to the incompressible Navier–Stokes equations.