Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system Abels, Helmut Fischer, Julian L ; https://orcid.org/0000-0002-0479-558X Moser, Maximilian ddc:510 We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility mε>0 in the Allen-Cahn equation tends to zero in a subcritical way, i.e., mε=m0εβ for some β∈(0,2) and m0>0 . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term mεHΓt in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow. Springer Nature 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/17887 https://research-explorer.ista.ac.at/download/17887/17938 Abels H, Fischer JL, Moser M. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. <i>Archive for Rational Mechanics and Analysis</i>. 2024;248(5). doi:<a href="https://doi.org/10.1007/s00205-024-02020-9">10.1007/s00205-024-02020-9</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-024-02020-9 info:eu-repo/semantics/altIdentifier/issn/0003-9527 info:eu-repo/semantics/altIdentifier/e-issn/1432-0673 info:eu-repo/semantics/altIdentifier/wos/001305530600001 info:eu-repo/semantics/altIdentifier/arxiv/2311.02997 info:eu-repo/semantics/altIdentifier/pmid/39239088 info:eu-repo/semantics/openAccess