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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids


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Table of Contents

Derivation Of Equations For Continuum Mechanics And Thermodynamics Of FluidsVariational Modeling And Complex FluidsThe Stokes Equation in the L p -setting: Well-posedness and Regularity PropertiesStokes Problems in Irregular Domains with Various Boundary ConditionsLeray's Problem on Existence of Steady State Solutions for the Navier-Stokes FlowStationary Navier-Stokes Flow in Exterior Domains and Landau SolutionsSteady-State Navier-Stokes Flow Around a Moving BodyStokes Semigroups, Strong, Weak, and Very Weak Solutions for General DomainsSelf-Similar Solutions to the Nonstationary Navier-Stokes EquationsTime-Periodic Solutions to the Navier-Stokes EquationsLarge Time Behavior of the Navier-Stokes FlowCritical Function Spaces for the Well-posedness of the Navier-Stokes Initial Value ProblemExistence and Stability of Viscous VorticesModels and Special Solutions of the Navier-Stokes EquationsThe Inviscid Limit and Boundary Layers for Navier-Stokes FlowsRegularity Criteria for Navier-Stokes SolutionsStable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler EquationsVorticity Direction and Regularity of Solutions to the Navier-Stokes EquationsRecent Advances Concerning Certain Class of Geophysical FlowsEquations for Polymeric MaterialsModeling of Two-Phase Flows With and Without Phase TransitionsEquations for Viscoelastic Fluids

Modeling and Analysis of the Ericksen-Leslie Equations for Nematic Liquid Crystal FlowsClassical Well-posedness of Free Boundary Problems in Viscous Incompressible Fluid MechanicsStability of Equilibrium Shapes in Some Free Boundary Problems Involving FluidsWeak Solutions and Diffuse Interface Models for Incompressible Two-Phase FlowsWater Waves With or Without Surface TensionConcepts of Solutions in the Thermodynamics of Compressible FluidsWeak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime BehaviorWeak Solutions for the Compressible Navier-Stokes Equations with Density Dependent ViscositiesWeak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical CasesWeak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity ClassSymmetric Solutions to the Viscous Gas EquationsLocal and Global Solutions for the Compressible Navier-Stokes Equations Near Equilibria Via the Energy MethodFourier Analysis Methods for the Compressible Navier-Stokes EquationsLocal and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria Via the Maximal RegularityLocal and Global Solvability of Free Boundary Problems for the Compressible Navier-Stokes Equations Near EquilibriaGlobal Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible FlowsGlobal Existence of Classical Solutions and Optimal Decay Rate for Compressible Flows Via the Theory of SemigroupsFinite Time Blow-up of Regular Solutions for Compressible FlowsBlow-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 DimensionWell-posedness of the IBVPs for the 1D Viscous Gas EquationsWaves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact WavesExistence of Stationary Weak Solutions for Isentropic and Isothermal Compressible FlowsExistence of Stationary Weak Solutions for Compressible Heat Conducting FlowsExistence and Uniqueness of Strong Stationary Solutions for Compressible FlowsLow Mach Number Limits and Acoustic WavesSingular Limits for Models of Compressible, Viscous, Heat Conducting, and/or Rotating FluidsScale Analysis of Compressible Flows from an Application PerspectiveWeak and Strong Solutions of Equations of Compressible MagnetohydrodynamicsMulti-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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