Abstract
where v > 0, 0 are the constant viscosity and density, n is the unit vector of the external normal to F ; ~ > 0 is the surface tension coefficient, D is the strain-rate tensor with elementsDij = ~ui/~x j + ~u./~xi)/2 (i, j = i, 2, 3); H is the mean curvature of the surface F t (it is considered that H j> 0 if F t is convex within the fluid; po, g are the given external pressure and the mass force vector. Condition (1.3) expresses the equality of all forces acting on the free boundary while (1.4) denotes that F t consists of the same particles (the equation f(x, t) = 0 gives the free boundary Ft).
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