Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension

2018/01/15 by Abels, Helmut, Daube, Johannes, Kraus, Christiane · 1 citation
#35Q30 #35Q35 #35R35 #76D05 #76D45 #76T99 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.04840

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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