Abstract
We consider the free boundary problem of the two-phase Navier-Stokes equation with surface tension and gravity in the whole space. We prove a local-in-time unique existence theorem in the space W 2,1 q,p with 2 < p < ∞ and n < q < ∞ for any initial data satisfying certain compatibility conditions. Our theorem is proved by the standard fixed point argument based on the maximal L p -L q regularity theorem for the corresponding linearized equations.
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