Some free boundary problem for two phase inhomogeneous incompressible flow

Hirokazu Saito, Yoshihiro Shibata, Xin Zhang

Research output: Contribution to journalArticlepeer-review


In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous ows with moving interfaces in Lp- Lqmaximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by Y.Shibata & S.Shimizu, we find the local solutions in Lp-Lqclass in some general uniform W2-1=rrdomain in ℝNby assuming (p; q)∈]2;∞[×]N;∞[ or (p; q) ∈]1; 2[×]N;∞[ satisfying 1/p+N/q > 3/2: In particular, less regular initial data are allowed by assuming p < 2: In addition, if the density and the viscosity coefficient are piecewise constant, we can construct the long time solution from the small initial states in the case of the bounded droplet. This is due to some decay property for the corresponding linearized problem.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Nov 6


  • Analytic semigroup
  • Inhomogeneous incompressible Navier-Stokes equations
  • L- Lmaximal regularity
  • Two-phase problem

ASJC Scopus subject areas

  • General

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