Authors:
- 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
Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)
Part of the book sub series: Lecture Notes in Mathematical Fluid Mechanics (LNMFM)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- 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
- Capillary forces fluid mechanics
Reviews
Authors and Affiliations
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Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
I. V. Denisova
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St. Petersburg Department of Steklov Math. Institute, Russian Academy of Sciences, St. Petersburg, Russia
V. A. Solonnikov
Bibliographic Information
Book Title: Motion of a Drop in an Incompressible Fluid
Authors: I. V. Denisova, V. A. Solonnikov
Series Title: Advances in Mathematical Fluid Mechanics
DOI: https://doi.org/10.1007/978-3-030-70053-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-70052-2Published: 21 September 2021
eBook ISBN: 978-3-030-70053-9Published: 20 September 2021
Series ISSN: 2297-0320
Series E-ISSN: 2297-0339
Edition Number: 1
Number of Pages: VII, 316
Number of Illustrations: 206 b/w illustrations, 2 illustrations in colour
Additional Information: Translation from Russian language edition: Dvizhenie kapli v neszhimaemoy zhidkosti: monografiya by I. V. Denisova and V. A. Solonnikov, © Izdatel'stvo lan' 2020, Izdatel'stvo lan'. All Rights Reserved.
Topics: Functional Analysis, Analysis, Mathematical Methods in Physics, Classical and Continuum Physics