Small-time existence for the Navier-Stokes equations with a free surface
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We prove the small-time existence of a solution of the Navier-Stokes equations, for any initial data, for a free boundary fluid with surface tension taken into account. A fixed point method is used. The linearized problem is hyperbolic and dissipative. The classical methods to solve it seem to fail and the method used here could perhaps be applied for equations of the same kind.
KeywordsSurface Tension Free Surface Initial Data System Theory Mathematical Method
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