JournalsifbVol. 2 , No. 4DOI 10.4171/ifb/27

A free-boundary problem for Stokes equations: classical solutions

  • Stanislav Antontsev

    Universidade de Lisboa, Portugal
  • Vadim Yurinsky

    Universidade da Beira Interior, Covilhã, Portugal
  • Anvarbek Meirmanov

    Belgorod State University, Russian Federation
A free-boundary problem for Stokes equations: classical solutions cover

Abstract

The problem considered is that of evolution of the free boundary separating two immiscible viscous fluids with different constant densities. The motion is described by the Stokes equations driven by the gravity force. For flows in a bounded domain &OHgr; ?n, n ? 2, we prove existence and uniqueness of classical solutions, and concentrate on the study of properties of the moving boundary separating the two fluids.