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The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Boundary value problems. --- Navier-Stokes equations. --- Physics. --- Navier-Stokes equations --- Boundary value problems --- Mathematics --- Mechanical Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Calculus --- Aeronautics Engineering & Astronautics --- Differential equations, Partial. --- Partial differential equations --- Boundary conditions (Differential equations) --- Equations, Navier-Stokes --- Mathematics. --- Partial differential equations. --- Mathematical physics. --- Partial Differential Equations. --- Mathematical Physics. --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Differential equations, partial. --- Physical mathematics --- Physics

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This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of  fluid flows modeling on the basis of a typical Navier-Stokes-Fourier  initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff  problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

Differential equations, Partial. --- Differential equations, partial. --- Differential equations, Partial -- Asymptotic theory. --- Engineering. --- Engineering mathematics. --- Hydraulic engineering. --- Differential equations, Partial --- Fluid mechanics --- Mathematics --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Applied Mathematics --- Civil Engineering --- Calculus --- Asymptotic theory --- Navier-Stokes equations. --- Equations, Navier-Stokes --- Atmospheric sciences. --- Partial differential equations. --- Fluids. --- Applied mathematics. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Partial Differential Equations. --- Atmospheric Sciences. --- Appl.Mathematics/Computational Methods of Engineering. --- Fluid dynamics --- Viscous flow --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Engineering, Hydraulic --- Hydraulics --- Shore protection --- Atmospheric sciences --- Earth sciences --- Atmosphere --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Hydromechanics --- Continuum mechanics