Pressure reconstruction for weak solutions of the two-phase incompressible Navier–Stokes equations with surface tension

Zusammenfassung

For the two-phase incompressible Navier-Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation.