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

Article type: Research Article

Authors: Abels, Helmut^{a; *} | Daube, Johannes^b | Kraus, Christiane^c

Affiliations: [a] Fakultät für Mathematik, Universität Regensburg, Universitätsstr. 31, 93053 Regensburg, Germany. E-mail: helmut.abels@ur.de | [b] Abteilung für Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg, Germany. Tel.: +49 (0)761 203-5639; Fax: +49 (0)761 203-5632. E-mail: johannes.daube@mathematik.uni-freiburg.de | [c] Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Germany. E-mail: kraus@wias-berlin.de

Correspondence: [*] Corresponding author. E-mail: helmut.abels@ur.de.

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.

Keywords: Fluid mechanics, Navier–Stokes equations, free boundary problems, surface tension

DOI: 10.3233/ASY-181507

Journal: Asymptotic Analysis, vol. 113, no. 1-2, pp. 51-86, 2019