Global Existence Of Strong Solutions To The Three Dimensional Incompressible Navier Stokes Equations With Special Boundary Conditions PDF Download
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Author | : Douglas A. Riley |
Publisher | : |
Total Pages | : 376 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Global Existence of Strong Solutions to the Three-dimensional Incompressible Navier-Stokes Equations with Special Boundary Conditions Book in PDF, ePub and Kindle
Author | : Wojciech M. Zajączkowski |
Publisher | : |
Total Pages | : 146 |
Release | : 2005 |
Genre | : Boundary value problems |
ISBN | : |
Download Global Special Regular Solutions to the Navier-Stokes Equations in Axially Symmetric Domains Under Boundary Slip Conditions Book in PDF, ePub and Kindle
Author | : Pierre-Louis Lions |
Publisher | : Clarendon Press |
Total Pages | : 252 |
Release | : 1996-06-27 |
Genre | : Science |
ISBN | : 9780198514879 |
Download Mathematical Topics in Fluid Mechanics: Volume 1: Incompressible Models Book in PDF, ePub and Kindle
One of the most challenging topics in applied mathematics over the past decades has been the development of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc. lead to such equations when formulated in mathematical terms. However despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contains many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena.
Author | : Guilong Gui |
Publisher | : Springer Science & Business Media |
Total Pages | : 173 |
Release | : 2013-04-13 |
Genre | : Mathematics |
ISBN | : 3642360289 |
Download Stability to the Incompressible Navier-Stokes Equations Book in PDF, ePub and Kindle
This thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.
Author | : Sergio Frigeri |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Download Strong Solutions to Nonlocal 2D Cahn-Hilliard-Navier-Stokes Systems with Nonconstant Viscosity, Degenerate Mobility and Singular Potential Book in PDF, ePub and Kindle
We consider a nonlinear system which consists of the incompressible Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We suppose that the viscosity depends smoothly on the order parameter as well as the mobility. Moreover, we assume that the mobility is degenerate at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with no-slip boundary condition for the (average) velocity and homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the two-dimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weak-strong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal Cahn-Hilliard equation, with a given velocity field, in the three dimensional case as well.
Author | : Hermann Sohr |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2012-12-13 |
Genre | : Mathematics |
ISBN | : 3034805519 |
Download The Navier-Stokes Equations Book in PDF, ePub and Kindle
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
Author | : James C. Robinson |
Publisher | : Cambridge University Press |
Total Pages | : 487 |
Release | : 2016-09-07 |
Genre | : Mathematics |
ISBN | : 1107019664 |
Download The Three-Dimensional Navier-Stokes Equations Book in PDF, ePub and Kindle
An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
Author | : Coleman duP. Donaldson |
Publisher | : |
Total Pages | : 64 |
Release | : 1960 |
Genre | : Navier-Stokes equations |
ISBN | : |
Download Behavior of Solutions of the Navier-Stokes Equations for a Complete Class of Three-dimensional Viscous Vortices Book in PDF, ePub and Kindle
Author | : Alain Miranville |
Publisher | : SIAM |
Total Pages | : 216 |
Release | : 2019-09-09 |
Genre | : Mathematics |
ISBN | : 1611975921 |
Download The Cahn–Hilliard Equation: Recent Advances and Applications Book in PDF, ePub and Kindle
This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Author | : Stuart Eames Rogers |
Publisher | : |
Total Pages | : 52 |
Release | : 1986 |
Genre | : Navier-Stokes equations |
ISBN | : |
Download Numerical Solution of the Incompressible Navier-Stokes Equations in Three-dimensional Generalized Curvilinear Coordinates Book in PDF, ePub and Kindle