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Author: H. B. DA Veiga Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
This paper considers the non-linear system of partial differential equation, describing the barotropic stationary motion of a compressible fluid, in a bounded region Omega. Assume that the total mass of fluid inside Omega is fixed, and equal to (m) abs. vol. Omega, where the mean density m is given. For small f and g, there exists a unique solution u(x), rho(x) in a neighborhood of (0, m). Here, u(x) is the field of velocities, rho(x) the density of the fluid, p(rho(x)) the pressure field, and f(x) the external force field (in the physical interesting case one has g = 0). Moreover, the solutions of system converge to the solution of the Navier-Stokes equation as lambda approaches + infinity, i.e. when the Mach number becomes small. The solution of the Navier-Stokes equations are the incompressible limit of the solutions of the compressible Navier-Stokes equations. The proofs given here, apply, without supplementary difficulties, in the context of Sobolev spaces H superscript k, p, and other functional spaces. The results can be extended to the heat depending case, too. Keywords: Non-linear partical differential equations; Viscous compressible fluid; Incompressible limit; Stationary solutions.
Author: H. B. DA Veiga Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
This paper considers the non-linear system of partial differential equation, describing the barotropic stationary motion of a compressible fluid, in a bounded region Omega. Assume that the total mass of fluid inside Omega is fixed, and equal to (m) abs. vol. Omega, where the mean density m is given. For small f and g, there exists a unique solution u(x), rho(x) in a neighborhood of (0, m). Here, u(x) is the field of velocities, rho(x) the density of the fluid, p(rho(x)) the pressure field, and f(x) the external force field (in the physical interesting case one has g = 0). Moreover, the solutions of system converge to the solution of the Navier-Stokes equation as lambda approaches + infinity, i.e. when the Mach number becomes small. The solution of the Navier-Stokes equations are the incompressible limit of the solutions of the compressible Navier-Stokes equations. The proofs given here, apply, without supplementary difficulties, in the context of Sobolev spaces H superscript k, p, and other functional spaces. The results can be extended to the heat depending case, too. Keywords: Non-linear partical differential equations; Viscous compressible fluid; Incompressible limit; Stationary solutions.
Author: H. Beirao da Veiga Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
This paper studies a system which describes the stationary motion of a given amount of a compressible heat conducting, viscous fluid in a bounded domain omega of R sub n, n> 2. Here u(x) is the velocity field, rho(x) is the density of the fluid, zeta(x) is the absolute temperature, f(x) and h(x) are the assigned external force field and heat sources per unit mass, and p(rho, zeta) is the pressure. In the physically significant case one has g = 0. We prove that for small data (f, g, h) there exists a unique solution (u, rho, zeta) of the problem in a neighborhood of (0, m, zeta sub 0); for arbitrarily large data the stationary solution does not exist in general. Moreover, we prove that (for barotropic flows) the stationary solution of the compressible Navier-Strokes equations, as the Mach number becomes small. Section 5 studies the equilibrium solutions for the system. (Author).
Author: Tujin Kim Publisher: Springer Nature ISBN: 3030786595 Category : Mathematics Languages : en Pages : 374
Book Description
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.
Author: Jose Francisco Rodrigues Publisher: CRC Press ISBN: 1000158039 Category : Mathematics Languages : en Pages : 282
Book Description
This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.
Author: Pierre-Louis Lions Publisher: Oxford University Press ISBN: 9780198514886 Category : Language Arts & Disciplines Languages : en Pages : 370
Book Description
Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.
Author: Pavel Plotnikov Publisher: Springer Science & Business Media ISBN: 3034803672 Category : Mathematics Languages : en Pages : 470
Book Description
The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the 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.
Author: John G. Trulio Publisher: ISBN: Category : Computer programming Languages : en Pages : 112
Book Description
This report investigates a numerical calculation of viscous compressible fluid flow around right circular cylinder using AFTON 2P computer code.
Author: C. M. Dafermos Publisher: CRC Press ISBN: 100010415X Category : Mathematics Languages : en Pages : 811
Book Description
This volume is an outcome of the EQUADIFF 87 conference in Greece. It addresses a wide spectrum of topics in the theory and applications of differential equations, ordinary, partial, and functional. The book is intended for mathematics and scientists.
Author: H. B. DA Veiga
Author: H. B. DA Veiga
Author: H. Beirao da Veiga
Author: Tujin Kim
Author: Jose Francisco Rodrigues
Author: Pierre-Louis Lions
Author: Pavel Plotnikov
Author: Stefan Hildebrandt
Author: Paolo Secchi
Author: John G. Trulio
Author: C. M. Dafermos