--- res: bibo_abstract: - We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Sebastian foaf_name: Hensel, Sebastian foaf_surname: Hensel foaf_workInfoHomepage: http://www.librecat.org/personId=4D23B7DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-7252-8072 - foaf_Person: foaf_givenName: Alice foaf_name: Marveggio, Alice foaf_surname: Marveggio foaf_workInfoHomepage: http://www.librecat.org/personId=25647992-AA84-11E9-9D75-8427E6697425 bibo_doi: 10.1007/s00021-022-00722-2 bibo_issue: '3' bibo_volume: 24 dct_date: 2022^xs_gYear dct_identifier: - UT:000834834300001 dct_isPartOf: - http://id.crossref.org/issn/1422-6928 - http://id.crossref.org/issn/1422-6952 dct_language: eng dct_publisher: Springer Nature@ dct_title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities@ ...