Preface; Acknowledgements; Contents; Contributors; Part I Multiphase Flows; 1 Nonconvergence of the Capillary Stress Functional for Solutions of the Convective Cahn-Hilliard Equation; 1.1 Introduction; 1.2 Notation and Basic Assumptions; 1.3 Nonconvergence Result; References; 2 On the Interface Formation Model for Dynamic Triple Lines; 2.1 Introduction; 2.2 Integral Balances; 2.3 Transport Theorems; 2.4 Local Balances; 2.5 Entropy Production and Closure Relations; 2.6 Isothermal Case with Vanishing Triple Line Mass; 2.7 Thermodynamical Consistency and Equilibria; References

3 Global Solvability of the Problem on Two-Phase Capillary Fluid Motion in the Oberbeck
Boussinesq Approximation3.1 Statement of the Problem and the Main Result; 3.2 An Energy Estimate of the Solution; 3.3 Linearized Problems; 3.4 Global Solvability of the Problem (3.1), (3.4), (3.3); 3.4.1 Conclusions; References; 4 Stability of Steady Flow Past a Rotating Body; 4.1 Motivation and Introduction; 4.2 Auxiliary Results; 4.3 The Main Theorem on Stability; References; 5 Asymptotic Structure of Steady Stokes Flow Around a Rotating Obstacle in Two Dimensions; 5.1 Introduction; 5.2 Results

5.3 Fundamental Solution5.4 Proof of Theorem 5.2.1; 5.5 Proof of Theorem 5.2.2; References; 6 Toward Understanding Global Flow Structure; 6.1 Introduction; 6.2 Phenomena; 6.2.1 Localized Convection Patterns in Binary Fluid Convection; 6.2.2 Localized Convection Patterns in Bioconvection; 6.2.3 Surface Switching; 6.3 Analysis Methods; 6.3.1 Orbit Analysis Applying Covariant Lyapunov Analysis; 6.3.2 Generating Cellular Automata Rule from Measurement Data Alone; 6.4 Concluding Remarks; References; 7 Mathematical and Numerical Analysis of the Rayleigh-Plesset and the Keller Equations

7.1 Introduction7.2 Mathematical Models for Motion of a Spherical Bubble; 7.2.1 The Rayleigh-Plesset Equation; 7.2.2 The Rayleigh-Plesset-Keller Equation; 7.3 Mathematical Analysis; 7.4 A Hamiltonian Formulation of the Rayleigh-Plesset-Keller Equation; 7.4.1 A Hamiltonian Formulation of the Rayleigh-Plesset Equation; 7.4.2 A Hamiltonian Formulation of the Keller-Herring Equation; 7.5 Discrete Gradient Schemes for the Rayleigh-Plesset and Keller Equations; 7.6 Numerical Results; 7.6.1 The Inviscid Rayleigh-Plesset Equation; 7.6.2 The Keller Equation; 7.7 Concluding Remarks; References

8 On the Amplitude Equation of Approximate Surface Waves on the Plasma-Vacuum Interface8.1 Introduction; 8.2 The Plasma-Vacuum Interface Problem; 8.3 The Asymptotic Expansion; 8.4 The First Order Equations; 8.5 The Second Order Equations; 8.5.1 The Second Order Equations in the Plasma Region; 8.5.2 The Second Order Equations in Vacuum; 8.5.3 The Second Order Jump Conditions; 8.5.4 The Kernel; 8.6 Noncanonical Variables and Well-Posedness; 8.6.1 Well-Posedness of the Amplitude Equation; 8.6.2 Regularity of the First Order Terms U(1),V(1); References