## Abstract

In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous ows with moving interfaces in L_{p}- L_{q}maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by Y.Shibata & S.Shimizu, we find the local solutions in L_{p}-L_{q}class in some general uniform W^{2-1=r}_{r}domain in ℝ^{N}by 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 language | English |
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Journal | Unknown Journal |

Publication status | Published - 2018 Nov 6 |

## Keywords

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

## ASJC Scopus subject areas

- General