Dr. Xian Liao - Publications



Zero-Mach Number System

We are interested in wellposedness issues for zero-Mach number gas dynamics system in the presence of heat conduction. Summary.pdf

  • R. Danchin and X. Liao On the wellposedness of the full low-Mach number limit system in general Besov spaces. Commun. Contemp. Math.: 2012,14(3),1250022, 47 pages. Download.
  • X. Liao A global existence result for a zero Mach number system. J. Math. Fluid Mech.: 2014,16(1),77-103. Download.
  • F. Fanelli and X. Liao The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces. Asymptot. Anal.: 2015,93,no.1-2,115-140. Download.
  • F. Fanelli and X. Liao Analysis of an inviscid zero-Mach number system in endpoint Besov spaces with finite-energy initial data. J. Differential Equations: 2015,259(10),5074-5114. Download.

  • Non-Newtonian Fluids

    We are interested in a peculiar non-Newtonian compressible fluid with bounded density. Summary.pdf

  • E. Feireisl, X. Liao and J. Málek Global weak solutions to a class of non-Newtonian compressible fluids. Math. Methods Appl. Sci.: 2015,38(16),3482-3494. Download.

  • Inhomogeneous Incompressible Fluids

    We are interested in the propagation of the regularities with jump density functions. Summary.pdf

  • X. Liao On the strong solutions of the nonhomogeneous incompressible Navier-Stokes equations in a thin domain. Differential Integral Equations: 2016,29,167-182. Download.
  • X. Liao and P. Zhang On the global regularity of 2D density patch for inhomogeneous incompressible viscous flow. Arch. Ration. Mech. Anal.: 2016,220(3),937-981. Download.
  • X. Liao and P. Zhang Global regularities of 2-D density patches for viscous inhomogeneous incompressible flow with general density: low regularity case. Accepted in Comm. Pure Appl. Math., arXiv:1604.07922. DownloadFullVersion.
  • X. Liao and P. Zhang Global regularities of 2-D density patches for viscous inhomogeneous incompressible flow with general density: high regularity case. arXiv:1604.07922. DownloadFullVersion.
  • X. Liao and Y. Liu On the global regularity of three dimensional density patch for inhomogeneous incompressible viscous flow. Accepted in Sci. China Math., arXiv:1606.05395.

  • Gross-Pitaevskii Equations

    We are interested in the Lax operators in the Gross-Pitaevskii equations. Summary.pdf

  • H. Koch and X. Liao Conserved energies for the one-dimensional Gross-Pitaevskii equation: small energy case. Download.