Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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.

• Part 0 Derivation of Equations for incompressible and compressible fluids.- Modeling.- Part I Incompressible fluids.- Stokes approximation.- Steady viscous Newtonian fluids.- Unsteady viscous Newtonian fluids.- Regularity of nonstationary Navier-Stokes flow.- Mathematical theory for turbulence.- Incompressible fluids with various effects.- Free boundary problems.- Part II Compressible Fluids.- Equations and various concepts of solutions in the thermodynamics of compressible fluids.- Solutions for the one dimensional flows in the non steady case.- Global existence of weak solutions in several dimensions and their qualitative properties.- Regularity theory in the multidimensional non steady case.- Existence theory for the compressible steady flows.- Scale analysis and hydrodynamic limits within the equations of compressible fluids.- Examples of coupled systems including compressible fluids.