PreprintCC BY 4.0arXiv
Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion
Abstract
We study the initial-boundary value problem for the Cahn-Hilliard equation with degenerate mobility and singular diffusion at pure phases. This model describes the dynamics of phase separation in polymer blends with associated Flory-Huggins-de Gennes free energy. We prove the existence of global weak solutions in three-dimensional bounded and smooth domains, assuming that the initial datum has finite energy. We show the classical regularity in L2(0,T;H2(Ω)) for both the solution u and the function ϕ(u)=arcsin(u) through entropy estimates. In addition, when Ω is convex, a new elliptic-type argument yields the refined regularity u, ϕ(u) ∈ L4(0,T; H2(Ω)).
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BibTeX
@misc{conti2026global,
title = {{Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion}},
author = {Monica Conti and Andrea Giorgini and Greta Ricchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.06371},
eprint = {2608.06371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06371},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion
AU - Monica Conti
AU - Andrea Giorgini
AU - Greta Ricchi
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.06371
UR - https://arxiv.org/abs/2608.06371
AB - We study the initial-boundary value problem for the Cahn-Hilliard equation with degenerate mobility and singular diffusion at pure phases. This model describes the dynamics of phase separation in polymer blends with associated Flory-Huggins-de Gennes free energy. We prove the existence of global weak solutions in three-dimensional bounded and smooth domains, assuming that the initial datum has finite energy. We show the classical regularity in L^2(0,T;H^2(Ω)) for both the solution u and the function ϕ(u)=arcsin(u) through entropy estimates. In addition, when Ω is convex, a new elliptic-type argument yields the refined regularity u, ϕ(u) ∈ L^4(0,T; H^2(Ω)).
ER -