Mathematical Fluid Dynamics, Present and Future

1. Front Matter

   Pages i-xix

   PDF

2. Multiphase Flows

   1. Front Matter

      Pages 1-1

      PDF

   2. Nonconvergence of the Capillary Stress Functional for Solutions of the Convective Cahn-Hilliard Equation

      • Helmut Abels, Stefan Schaubeck

      Pages 3-23

   3. On the Interface Formation Model for Dynamic Triple Lines

      • Dieter Bothe, Jan Prüss

      Pages 25-47

   4. Global Solvability of the Problem on Two-Phase Capillary Fluid Motion in the Oberbeck–Boussinesq Approximation

      • Irina Vlad. Denisova

      Pages 49-70

   5. Stability of Steady Flow Past a Rotating Body

      • Giovanni Paolo Galdi, Jiří Neustupa

      Pages 71-94

   6. Asymptotic Structure of Steady Stokes Flow Around a Rotating Obstacle in Two Dimensions

      • Toshiaki Hishida

      Pages 95-137

   7. Toward Understanding Global Flow Structure

      • Makoto Iima, Takayuki Yamaguchi, Takeshi Watanabe, Akane Kawaharada, Yuji Tasaka, Erika Shoji

      Pages 139-158

   8. Mathematical and Numerical Analysis of the Rayleigh-Plesset and the Keller Equations

      • Masashi Ohnawa, Yukihito Suzuki

      Pages 159-180

   9. On the Amplitude Equation of Approximate Surface Waves on the Plasma-Vacuum Interface

      • Paolo Secchi

      Pages 181-201

   10. On the \({\mathscr {R}}\)-Bounded Solution Operator and the Maximal \(L_p\)-\(L_q\) Regularity of the Stokes Equations With Free Boundary Condition

       • Yoshihiro Shibata

       Pages 203-285

   11. On the Solvability of Free Boundary Problem for Viscous Compressible Fluids in an Infinite Time Interval

       • Vsevolod Alekseevich Solonnikov

       Pages 287-315

   12. Classical Solvability of the Two-Phase Radial Viscous Fingering Problem in a Hele-Shaw Cell

       • Atusi Tani, Hisasi Tani

       Pages 317-348

   13. Investigation of Bubble Clouds in a Cavitating Jet

       • Katsuhiro Yamamoto

       Pages 349-373

3. Other Related Topics

   1. Front Matter

      Pages 375-375

      PDF

   2. Weak Solutions to Problems Involving Inviscid Fluids

      • Eduard Feireisl

      Pages 377-399

   3. Enstrophy Variations in the Incompressible 2D Euler Flows and \(\alpha \) Point Vortex System

      • Takeshi Gotoda, Takashi Sakajo

      Pages 401-431

   4. Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows

      • Matthias Hieber, Jan Prüss

      Pages 433-459

   5. Statistical Mechanics of Quasi-geostrophic Vortices

      • Takeshi Miyazaki, Yuichi Shimoda, Keisei Saga

      Pages 461-486

   6. Heat Convection of Compressible Viscous Fluids. III

      • Takaaki Nishida, Mariarosaria Padula, Yoshiaki Teramoto

      Pages 487-495

This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

• MSC2010: 76-XX, 76T10, 76D05, 76D03, 35Q30
• Dynamical systems
• Mathematical fluid dynamics
• Multiphase flows
• Navier-Stokes equations
• Proceedings
• partial differential equations

• Department of Mathematics, Waseda University, Tokyo, Japan

  Yoshihiro Shibata, Yukihito Suzuki

Policies and ethics