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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.
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.
This introduction to the singularly perturbed methods in the
nonlinear elliptic partial differential equations emphasises the
existence and local uniqueness of solutions exhibiting
concentration property. The authors avoid using sophisticated
estimates and explain the main techniques by thoroughly
investigating two relatively simple but typical non-compact
elliptic problems. Each chapter then progresses to other related
problems to help the reader learn more about the general theories
developed from singularly perturbed methods. Designed for PhD
students and junior mathematicians intending to do their research
in the area of elliptic differential equations, the text covers
three main topics. The first is the compactness of the minimization
sequences, or the Palais-Smale sequences, or a sequence of
approximate solutions; the second is the construction of peak or
bubbling solutions by using the Lyapunov-Schmidt reduction method;
and the third is the local uniqueness of these solutions.
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