Energy equality for weak solutions of the compressible Navier–Stokes–Korteweg equations with general pressure law in a bounded domain

Abstract

In this paper, we study the energy equality for weak solutions to the compressible Navier–Stokes–Korteweg equations with general pressure law in a bounded domain Ω⊂Rd (d=2,3). By exploring the special structure of the nonlinear terms, and using coarea formula, we formulate the sufficient conditions for the regularity of weak solutions to ensure that energy equality holds.

Keywords

• Navier–Stokes–Korteweg equations
• Regularity
• Energy equality
• Bounded domain