Motion of a Drop an Incompressible Fluid

The authors’ main focus is on the evolution of an isolated mass with and without surface tension on the free interface. Using the Lagrange and Hanzawa transformations, local well-posedness in the Hölder and Sobolev–Slobodeckij on spaces is proven as well. Global well-posedness for small data is also proven, as is the well-posedness and stability of the motion of two phase fluid in a bounded domain. will appeal to researchers and graduate students working in the fields of mathematical hydrodynamics, the analysis of partial differential equations, and related topics.