Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids


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About the Book

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.

Table of Contents:
Derivation Of Equations For Continuum Mechanics And Thermodynamics Of Fluids Variational Modeling And Complex Fluids The Stokes Equation in the L p -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 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 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 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

About the Author :
Yoshikazu Giga is Professor at the Graduate School of Mathematical Sciences of the University of Tokyo, Japan. He is a fellow of the American Mathematical Society as well as of the Japan Society for Industrial and Applied Mathematics. Through his more than two hundred papers and two monographs, he has substantially contributed to the theory of parabolic partial differential equations including geometric evolution equations, semilinear heat equations as well as the incompressible Navier-Stokes equations. He has received several prizes including the Medal of Honour with Purple Ribbon from the government of Japan. Antonin Novotny is Professor at the Department of Mathematics of the University of Toulon and member of the Institute of Mathematics of the University of Toulon, France. Co-author of more than hundred papers and two monographs, he is one of the leading experts in the theory of compressible Navier-Stokes equations.


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Product Details
  • ISBN-13: 9783319133454
  • Publisher: Springer International Publishing AG
  • Publisher Imprint: Springer International Publishing AG
  • Height: 235 mm
  • No of Pages: 3045
  • Width: 155 mm
  • ISBN-10: 3319133454
  • Publisher Date: 08 May 2018
  • Binding: SA
  • Language: English
  • Returnable: Y


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