Axisymmetric solutions to coupled Navier-Stokes/Allen-Cahn equations?

Xiang Xu, Liyun Zhao, Chun Liu

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We investigate a family of axisymmetric solutions to a coupling of Navier-Stokes and Allen-Cahn equations in R3. First, a one-dimensional system of equations is derived from the method of separation of variables, which approximates the three-dimensional system along its symmetry axis. Then based on them, by adding perturbation terms, we construct finite energy solutions to the three-dimensional system. We prove the global regularity of the constructed solutions in both large viscosity and small initial data cases. These solutions can be considered as perturbations near infinite-energy solutions.

Original languageEnglish (US)
Pages (from-to)2246-2282
Number of pages37
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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