Mathematical Tools for the Study of the Incompressible Navier Stokes Equations and Related Models Preface Contents The equations of fluid mechanics Analysis tools Sobolev spaces Steady Stokes equations Navier Stokes equations for homogeneous fluids Nonhomogeneous fluids Boundary conditions modeling Classic differential operators Thermodynamics supplement References Index. The objective of this self contained book is two fold. First the reader is introduced to the modelling and mathematical analysis used in fluid mechanics especially concerning the Navier Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations in particular nonlinear evolution problems. The background needed are basic results in calculus integration and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless the authors’ aim is that graduate or PhD students as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics can find a detailed introduction to this subject.