Wellposedness and Regularity Estimates for Stochastic Cahn–Hilliard Equation with Unbounded Noise Diffusion

Jianbo Cui, Jialin Hong

Research output: Journal article publicationJournal articleAcademic researchpeer-review


In this article, we consider the one dimensional stochastic Cahn–Hilliard equation driven by multiplicative space-time white noise with diffusion coefficient of sublinear growth. By introducing the spectral Galerkin method, we obtain the well-posedness of the approximated equation in finite dimension. Then with help of the semigroup theory and the factorization method, the approximation processes are shown to possess many desirable properties. Further, we show that the approximation process is strongly convergent in a certain Banach space with an explicit algebraic convergence rate. Finally, the global existence and regularity estimates of the unique solution process are proven by means of the strong convergence of the approximation process, which fills a gap on the global existence of the mild solution for stochastic Cahn–Hilliard equation when the diffusion coefficient satisfies a growth condition of order α∈(13,1).

Original languageEnglish
Pages (from-to)1635-1671
Number of pages37
JournalStochastics and Partial Differential Equations: Analysis and Computations
Issue number4
Early online dateDec 2023
Publication statusE-pub ahead of print - Dec 2023


  • Global existence
  • Regularity estimate
  • Spectral Galerkin method
  • Stochastic Cahn–Hilliard equation
  • Unbounded noise diffusion

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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