Equations of Motion for Incompressible Viscous Fluids

This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors' approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.

Presents a variety of boundary conditions for fluids while taking into special account the properties of boundaries of vector fields on domains Highlights how fluid equations at the cutting edge of research were developed and how certain boundary conditions apply to various real-world problems Adopts a self-contained approach that covers introductory topics as well as more advanced material, such as friction conditions and a thorough outline of the Navier-Stokes equations

Inhalt
Miscellanea of Analysis.- Fluid Equations.- The Steady Navier-Stokes System.- The Non-steady Navier-Stokes System.- The Steady Navier-Stokes System with Friction Boundary Conditions.- The Non-steady Navier-Stokes System with Friction Boundary Conditions.- The Steady Boussinesq System.- The Non-steady Boussinesq System.- The Steady Equations for Heat-conducting Fluids.- The Non-steady Equations for Heat-conducting Fluids.