@article{17887,
  abstract     = {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.},
  author       = {Abels, Helmut and Fischer, Julian L and Moser, Maximilian},
  issn         = {1432-0673},
  journal      = {Archive for Rational Mechanics and Analysis},
  number       = {5},
  publisher    = {Springer Nature},
  title        = {{Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system}},
  doi          = {10.1007/s00205-024-02020-9},
  volume       = {248},
  year         = {2024},
}