{
  "annotation_id": "7a16bbfc-be54-47bf-8ccb-146ebaa17065",
  "date_created": "2026-02-17T05:53:15.902000Z",
  "date_modified": "2026-02-17T05:53:15.902000Z",
  "file_hash": "73662b16b4ed2151946763c629b7c966a319fad3ce71e06d8e4cfcf0efb2f1f5",
  "private": false,
  "record": {
    "abstract": "In [Cheng, Lasarzik, Thomas 2025 ARXIV-Preprint 2509.25508], we studied a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids in the framework of dissipative solutions using a logarithmic potential for the phase-field variable. This choice of potential has the effect that the fluid mixture cannot fully separate into two pure phases. The notion of dissipative solutions is based on a relative energy-dissipation inequality featuring a suitable regularity weight. In this way, this is a very weak solution concept. In the present work, we study the well-posedness of the geodynamical two-phase flow in the notion of energy-variational solutions. They feature an additional scalar energy variable that majorizes the system energy along solutions and they are further characterized by a variational inequality that combines an energy-dissipation estimate with the weak formulation of the system adding an error term that accounts for the mismatch between the energy variable and the system energy multiplied by a suitable regularity weight. We give a comparison of these two concepts. We further study different phase-field potentials for the geodynamical two-phase flow model. In particular, we address the variational limit from a potential with a logarithmic contribution to a double-obstacle potential, then also allowing for the emergence of pure phases. This study underlines that, thanks to its structure, the energy-variational solution is better suited for variational convergence methods than the dissipative solution.",
    "arxiv_id": "2601.08625",
    "authors": [
      "Fan Cheng",
      "Robert Lasarzik",
      "Marita Thomas"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Energy-variational solutions for geodynamical two-phase flows -- From logarithmic to double-obstacle potentials by variational convergence",
    "url": "https://arxiv.org/abs/2601.08625",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "96d17c22-7742-44b6-aa86-964706f04266",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}