Pressure reconstruction for weak solutions of the two-phase incompressible Navier--Stokes equations with surface tension
- Abels, Helmut
- Daube, Johannes
- Kraus, Christiane
2010 Mathematics Subject Classification
- 76T99 35Q30 35Q35, 35R35, 76D05, 76D45
- Fluid mechanics, Navier--Stokes equations, free boundary problems, surface tension
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.