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Peer-reviewedCC BYNonlinearity

Regularity of a bulk-surface Cahn–Hilliard model driven by Leray velocity fields

  • Andrea Giorgini1
  • Patrik Knopf2
  • Jonas Stange2
  1. 1Politecnico di Milano
  2. 2Universität Regensburg
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Abstract

We consider a convective bulk-surface Cahn–Hilliard system with dynamic boundary conditions and singular potentials. For this model, well-posedness results concerning weak and strong solutions have already been established in the literature. However, they require the prescribed velocity fields to belong to function spaces with high time regularity. In this paper, we prove that the well-posedness of weak solutions holds true under more general regularity assumptions on the velocity fields. Next, via an alternative proof for higher regularity, we show the well-posedness of strong solutions for velocity fields of Leray type, which is a more relevant assumption for physical applications. Our approach hinges upon a new well-posedness and regularity theory for a bulk-surface elliptic system with singular nonlinearities, which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@article{giorgini2026regularity,
  title = {{Regularity of a bulk-surface Cahn–Hilliard model driven by Leray velocity fields}},
  author = {Andrea Giorgini and Patrik Knopf and Jonas Stange},
  journal = {Nonlinearity},
  year = {2026},
  month = aug,
  doi = {10.1088/1361-6544/ae8e1b},
  url = {https://doi.org/10.1088/1361-6544/ae8e1b},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Regularity of a bulk-surface Cahn–Hilliard model driven by Leray velocity fields
AU  - Andrea Giorgini
AU  - Patrik Knopf
AU  - Jonas Stange
PY  - 2026
DA  - 2026/08/11
JO  - Nonlinearity
DO  - 10.1088/1361-6544/ae8e1b
UR  - https://doi.org/10.1088/1361-6544/ae8e1b
AB  - We consider a convective bulk-surface Cahn–Hilliard system with dynamic boundary conditions and singular potentials. For this model, well-posedness results concerning weak and strong solutions have already been established in the literature. However, they require the prescribed velocity fields to belong to function spaces with high time regularity. In this paper, we prove that the well-posedness of weak solutions holds true under more general regularity assumptions on the velocity fields. Next, via an alternative proof for higher regularity, we show the well-posedness of strong solutions for velocity fields of Leray type, which is a more relevant assumption for physical applications. Our approach hinges upon a new well-posedness and regularity theory for a bulk-surface elliptic system with singular nonlinearities, which may be of independent interest.
SN  - 0951-7715
SN  - 1361-6544
ER  -