---
res:
  bibo_abstract:
  - "This thesis concerns the application of variational methods to the study of evolution
    problems arising in fluid mechanics and in material sciences. The main focus is
    on weak-strong stability properties of some curvature driven interface evolution
    problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase
    mean curvature flow, and on the phase-field approximation of the latter. Furthermore,
    we discuss a variational approach to the study of a class of doubly nonlinear
    wave equations.\r\nFirst, we consider the two-phase Navier–Stokes flow with surface
    tension within a bounded domain. The two fluids are immiscible and separated by
    a sharp interface, which intersects the boundary of the domain at a constant contact
    angle of ninety degree. We devise a suitable concept of varifolds solutions for
    the associated interface evolution problem and we establish a weak-strong uniqueness
    principle in case of a two dimensional ambient space. In order to focus on the
    boundary effects and on the singular geometry of the evolving domains, we work
    for simplicity in the regime of same viscosities for the two fluids.\r\nThe core
    of the thesis consists in the rigorous proof of the convergence of the vectorial
    Allen-Cahn equation towards multiphase mean curvature flow for a suitable class
    of multi- well potentials and for well-prepared initial data. We even establish
    a rate of convergence. Our relative energy approach relies on the concept of gradient-flow
    calibration for branching singularities in multiphase mean curvature flow and
    thus enables us to overcome the limitations of other approaches. To the best of
    the author’s knowledge, our result is the first quantitative and unconditional
    one available in the literature for the vectorial/multiphase setting.\r\nThis
    thesis also contains a first study of weak-strong stability for planar multiphase
    mean curvature flow beyond the singularity resulting from a topology change. Previous
    weak-strong results are indeed limited to time horizons before the first topology
    change of the strong solution. We consider circular topology changes and we prove
    weak-strong stability for BV solutions to planar multiphase mean curvature flow
    beyond the associated singular times by dynamically adapting the strong solutions
    to the weak one by means of a space-time shift.\r\nIn the context of interface
    evolution problems, our proofs for the main results of this thesis are based on
    the relative energy technique, relying on novel suitable notions of relative energy
    functionals, which in particular measure the interface error. Our statements follow
    from the resulting stability estimates for the relative energy associated to the
    problem.\r\nAt last, we introduce a variational approach to the study of nonlinear
    evolution problems. This approach hinges on the minimization of a parameter dependent
    family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy
    (WIDE) functionals. We consider a class of doubly nonlinear wave equations and
    establish the convergence, up to subsequences, of the associated WIDE minimizers
    to a solution of the target problem as the parameter goes to zero.@eng"
  bibo_authorlist:
  - 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: 10.15479/at:ista:14587
  dct_date: 2023^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: Weak-strong stability and phase-field approximation of interface evolution
    problems in fluid mechanics and in material sciences@
...