Motion of a Drop in an Incompressible Fluid

“The book provides a profound introduction into recent developments of the mathematical theory of incompressible two-phase flows and outlines multitude of contributions by two outstanding experts in this field.” (Thomas Eiter, zbMATH 1511.76002, 2023)

• Introduction.- A Model Problem with Plane Interface and with Positive Surface Tension Coefficient.- The Model Problem Without Surface Tension Forces.- A Linear Problem with Closed Interface Under Nonnegative Surface Tension.- Local Solvability of the Problem in Weighted Hölder Spaces.- Global Solvability in the Hölder Spaces for the Nonlinear Problem without Surface Tension.- Global Solvability of the Problem Including Capillary Forces. Case of the Hölder Spaces.- Thermocapillary Convection Problem.- Motion of Two Fluids in the Oberbeck - Boussinesq Approximation.- Local L2-solvability of the Problem with Nonnegative Coefficient of Surface Tension.- Global L2-solvability of the Problem without Surface Tension.- L2-Theory for Two-Phase Capillary Fluid.