Springer, 2018. — 3035 p. — (Springer Reference). — ISBN 3319133438.Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids. Contents Volume 1 Derivation of Equations for Incompressible and Compressible Fluids Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids Variational Modeling and Complex Fluids Incompressible Fluids The Stokes Equation in the Lp-Setting: Well-Posedness and Regularity Properties Stokes Problems in Irregular Domains with Various Boundary Conditions Leray’s Problem on Existence of Steady-State Solutions for the Navier-Stokes Flow Stationary Navier-Stokes Flow in Exterior Domains and Landau Solutions Steady-State Navier-Stokes Flow Around a Moving Body Stokes Semigroups, Strong, Weak, and Very Weak Solutions for General Domains Self-Similar Solutions to the Nonstationary Navier-Stokes Equations Time-Periodic Solutions to The Navier-Stokes Equations Large Time Behavior of the Navier-Stokes Flow Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem Existence and Stability of Viscous Vortices Models and Special Solutions of the Navier-Stokes Equations The Inviscid Limit and Boundary Layers for Navier-Stokes Flows Regularity Criteria for Navier-Stokes Solutions Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations Recent Advances Concerning Certain Class of Geophysical Flows Equations for Polymeric Materials Contents Volume 2 Modeling of Two-Phase Flows With and Without Phase Transitions Equations for Viscoelastic Fluids Modeling and Analysis of the Ericksen-Leslie Equations for Nematic Liquid Crystal Flows Classical Well-Posedness of Free Boundary Problems in Viscous Incompressible Fluid Mechanics Stability of Equilibrium Shapes in Some Free Boundary Problems Involving Fluids Weak Solutions and Diffuse Interface Models for Incompressible Two-Phase Flows Water Waves with or Without Surface Tension Compressible Viscous Fluids Concepts of Solutions in the Thermodynamics of Compressible Fluids Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior Weak Solutions for the Compressible Navier-Stokes Equations with Density Dependent Viscosities Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class Symmetric Solutions to the Viscous Gas Equations Local and Global Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Energy Method Fourier Analysis Methods for the Compressible Navier-Stokes Equations Local and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Maximal Regularity Local and Global Solvability of Free Boundary Problems for the Compressible Navier-Stokes Equations Near Equilibria Contents Volume 3 Global Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible Flows Global Existence of Classical Solutions and Optimal Decay Rate for Compressible Flows via the Theory of Semigroups Finite Time Blow-Up of Regular Solutions for Compressible Flows Blow-Up Criteria of Strong Solutions and Conditional Regularity of Weak Solutions for the Compressible Navier-Stokes Equations Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension Well-Posedness of the IBVPs for the 1D Viscous Gas Equations Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows Existence of Stationary Weak Solutions for Compressible Heat Conducting Flows Existence and Uniqueness of Strong Stationary Solutions for Compressible Flows Low Mach Number Limits and Acoustic Waves Singular Limits for Models of Compressible, Viscous, Heat Conducting, and/or Rotating Fluids Scale Analysis of Compressible Flows from an Application Perspective Weak and Strong Solutions of Equations of Compressible Magnetohydrodynamics Multi-Fluid Models Including Compressible Fluids Solutions for Models of Chemically Reacting Compressible Mixtures
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