Global classical solution to three-component Cahn-Hilliard phase-field model

Ning Duan; Yinghao Wang; Ning Duan; Yinghao Wang

doi:10.3934/math.2026027

AIMS Mathematics

2026, Volume 11, Issue 1: 618-643. doi: 10.3934/math.2026027

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Research article

Global classical solution to three-component Cahn-Hilliard phase-field model

Ning Duan ^,,
Yinghao Wang

College of Sciences, Northeastern University, Shenyang 110004, China

Received: 24 October 2025 Revised: 24 December 2025 Accepted: 30 December 2025 Published: 08 January 2026
MSC : 35A01, 35B45, 35K55

The main purpose of this paper was to study the global existence for the Cauchy problem for three-component Cahn-Hilliard phase-field model in 2D whole space. We first constructed the local classical solutions, then by combining some a priori estimates and the continuity argument, the local classical solutions were extended step by step to all $ t > 0 $.
- global existence,
- Cauchy problem,
- three-component Cahn-Hilliard equation,
- local solution,
- continuity argument
Citation: Ning Duan, Yinghao Wang. Global classical solution to three-component Cahn-Hilliard phase-field model[J]. AIMS Mathematics, 2026, 11(1): 618-643. doi: 10.3934/math.2026027

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Abstract

The main purpose of this paper was to study the global existence for the Cauchy problem for three-component Cahn-Hilliard phase-field model in 2D whole space. We first constructed the local classical solutions, then by combining some a priori estimates and the continuity argument, the local classical solutions were extended step by step to all $ t > 0 $.

References

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