Abstract:We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on Lp-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data we show the differentiability of the solution with respect to initial and distributed controls for appropriate spaces resulting form the Lp-maximal regularity setting. We consider first a formulation, where the interface is transformed to a hyperplane. Then we deduce differenti… Show more
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