Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

ISBN-13: 9783319133430 / Angielski / Twarda / 2018 / 3045 str.

Yoshikazu Giga; Antonin Novotny

Opis

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. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.

Spis treści

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

O autorze

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.