WIAS Preprint No. 2662, (2019)

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



Authors

  • Abels, Helmut
  • Daube, Johannes
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 76T99 35Q30 35Q35, 35R35, 76D05, 76D45

Keywords

  • Fluid mechanics, Navier--Stokes equations, free boundary problems, surface tension

DOI

10.20347/WIAS.PREPRINT.2662

Abstract

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.

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