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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 2, pp 485–498 | Cite as

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

  • Y. Wang
  • J. XiaoEmail author
Article

Abstract

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 \(\mathbb {R}^{N\ge 2}\). 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).

Keywords

Nonnegative weak solution fractional Laplacian uniqueness 

Mathematics Subject Classification

35Q30 76D05 

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBeijingChina
  2. 2.School of MathematicsThe University of EdinburghEdinburghUnited Kingdom
  3. 3.Department of Mathematics and StatisticsMemorial UniversitySt. John’sCanada

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