A Liouville Problem for the Stationary Fractional Navier–Stokes–Poisson System

Yuzhao Wang, Jie Xiao

Research output: Contribution to journalArticlepeer-review


This paper deals with a Liouville problem for the stationary fractional Navier–Stokes–Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier–Stokes systems in RN≥2 . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre’s technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245–1260, 2007).
Original languageEnglish
JournalJournal of Mathematical Fluid Mechanics
Early online date21 Jun 2017
Publication statusE-pub ahead of print - 21 Jun 2017


  • Nonnegative weak solution
  • fractional Laplacian
  • uniqueness


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