We consider the motion of two superposed immiscible, viscous, incompressible, capillary fluids that are separated by a sharp interface which needs to be determined as part of the problem. Allowing for gravity to act on the fluids, we prove local well-posedness of the problem. In particular, we obtain well-posedness for the case where the heavy fluid lies on top of the light one, that is, for the case where the Rayleigh-Taylor instability is present. Additionally we show that solutions become real analytic instantaneously.
CITATION STYLE
Prüss, J., & Simonett, G. (2011). Analytic solutions for the two-phase navier-stokes equations with surface tension and gravity. In Progress in Nonlinear Differential Equations and Their Application (Vol. 80, pp. 507–540). Springer US. https://doi.org/10.1007/978-3-0348-0075-4_26
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