On The Stationary Motion Of Compressible Viscous Fluids
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Stationary Motions and Incompressible Limit for Compressible Viscous Fluids
Author | : H. B. DA Veiga |
Publisher | : |
Total Pages | : 27 |
Release | : 1985 |
Genre | : |
ISBN | : |
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.
Equations of Motion for Incompressible Viscous Fluids
Author | : Tujin Kim |
Publisher | : Springer Nature |
Total Pages | : 374 |
Release | : 2021-09-09 |
Genre | : Mathematics |
ISBN | : 3030786595 |
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.
Dynamics of Viscous Compressible Fluids
Author | : Eduard Feireisl |
Publisher | : Oxford University Press |
Total Pages | : 228 |
Release | : 2004 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780198528388 |
This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.
Viscous and Compressible Fluid Dynamics
Author | : Michael Edward O'Neill |
Publisher | : |
Total Pages | : 408 |
Release | : 1989 |
Genre | : Fluid dynamics |
ISBN | : |
Textbooks for students of applied mathematics, engineers, and useful for meteorologists. Introduction to the theory of fluid mechanics, companion to same authors' Ideal and incompressible fluid dynamics. Some prior knowledge of ideal compressiblity is desirable. Much of the basic mathematical techniques is included. Annotation copyrighted by Book News, Inc., Portland, OR
Mathematical Topics in Fluid Mechanics
Author | : Jose Francisco Rodrigues |
Publisher | : CRC Press |
Total Pages | : 280 |
Release | : 2020-10-02 |
Genre | : Mathematics |
ISBN | : 1000115232 |
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.
Initial Boundary Value Problems for the Equations of Motion of Compressible Viscous and Heat-Conductive Fluids
Author | : Akitaka Matsumura |
Publisher | : |
Total Pages | : 33 |
Release | : 1982 |
Genre | : |
ISBN | : |
The equations of motion of compressible viscous and heat-conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region. The global solution in time is proved to exist uniquely and approach the stationary state as t approaches infinity, provided the prescribed initial data and the external force are sufficiently small. (Author).
Numerical Calculations of Viscous Compressible Fluid Flow Around a Stationary Cylinder
Author | : John G. Trulio |
Publisher | : |
Total Pages | : 112 |
Release | : 1970 |
Genre | : Computer programming |
ISBN | : |
This report investigates a numerical calculation of viscous compressible fluid flow around right circular cylinder using AFTON 2P computer code.
An L(p)-Theory for the N-Dimensional, Stationary, Compressible, Navier-Stokes Equations, and the Incompressible Limit for Compressible Fluids. The Equilibrium Solutions
Author | : H. Beirao da Veiga |
Publisher | : |
Total Pages | : 33 |
Release | : 1986 |
Genre | : |
ISBN | : |
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).