On the two-phase Navier–Stokes equations with surface tension

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<jats:p> The two-phase free boundary problem for the Navier–Stokes system is considered in a situation where the initial interface is close to a halfplane. By means of <jats:italic>Lp</jats:italic> -maximal regularity of the underlying linear problem we show local well-posedness of the problem, and prove that the solution, in particular the interface, becomes instantaneously real analytic. </jats:p>

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