Motion of a Drop in an Incompressible Fluid
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Beschreibung
This mathematical monograph details the authors' results on solutions to problems governing the simultaneous motion of two incompressible fluids. Featuring a thorough investigation of the unsteady motion of one fluid in another, researchers will find this to be a valuable resource when studying non-coercive problems to which standard techniques cannot be applied. As authorities in the area, the authors offer valuable insight into this area of research, which they have helped pioneer. This volume will offer pathways to further research for those interested in the active field of free boundary problems in fluid mechanics, and specifically the two-phase problem for the Navier-Stokes equations.
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 L2 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.
Motion of a Drop in an Incompressible Fluid will appeal to researchers and graduate students working in the fields of mathematical hydrodynamics, the analysis of partial differential equations, and related topics.
This mathematical monograph details the authors' results on solutions to problems governing the simultaneous motion of two incompressible fluids. Featuring a thorough investigation of the unsteady motion of one fluid in another, researchers will find this to be a valuable resource when studying non-coercive problems to which standard techniques cannot be applied. As authorities in the area, the authors offer valuable insight into this area of research, which they have helped pioneer. This volume will offer pathways to further research for those interested in the active field of free boundary problems in fluid mechanics, and specifically the two-phase problem for the Navier-Stokes equations.
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 L2 spaces is proven as well. Globalwell-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.
Motion of a Drop in an Incompressible Fluid will appeal to researchers and graduate students working in the fields of mathematical hydrodynamics, the analysis of partial differential equations, and related topics.
Features proofs from leading researchers in the mathematical analysis of fluids, including a global-in-time solution to the problem of the motion of a drop in a liquid medium in a container for small data Explores the smoothness of solutions to problems governing the simultaneous motion of two incompressible fluids Offers pathways to further research for those interested in this active area
Autor*in
I. V. Denisova
Themen in »Motion of a Drop in an Incompressible Fluid«
Free boundary problems Boundary value problems Viscous incompressible fluids Two-phase fluid Interface problems Navier-Stokes equations Sobolev-Slobodetskiy functional spaces Hoelder spaces Hoelder inequality Existence initial boundary value problem Uniqueness initial boundary value problem Thermocapillary convection Oberbek-Boussinesq approximation L2 solvability boundary value problem Two-phase capillary fluid
Stimmen zu »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)
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