Mathematical Models in Boundary Layer TheorySince Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise. |
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Contents
The NavierStokes Equations and the Prandtl System | 1 |
von Mises Variables | 20 |
Crocco Variables | 82 |
Nonstationary Boundary Layer | 153 |
Formation of the Boundary Layer | 265 |
Finite Difference Method | 318 |
Diffraction Problems for the Prandtl System | 340 |
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Common terms and phrases
According Assume assumptions asymptotic attains boundary conditions boundary layer bounded choose chosen coefficient consider consider the function const constructed continuous convergence corresponding defined depend derivatives difference differential equations domain dx dy equal equation established estimate existence expression flow fluid following equation following inequalities following properties function given Hence hold Hölder imply inequality integral interval introduce Lemma Let us show limit maximum principle method Moreover negative obtain the following pass pm,k positive constants Prandtl system Proof proved relation respect result satisfies satisfies the inequality Sect side similar smooth solution of problem sufficiently large sufficiently small Theorem tions transformation uniqueness uo(y variables vo(x weak solution wm,k ди др ду дх
Bibliographic information
| Title | Mathematical Models in Boundary Layer Theory Volume 15 of Applied Mathematics |
| Authors | O.A. Oleinik, V.N. Samokhin |
| Edition | illustrated |
| Publisher | CRC Press, 1999 |
| ISBN | 1584880155, 9781584880158 |
| Length | 528 pages |
| Subjects | › › Mathematics / Applied Mathematics / Differential Equations / General Mathematics / General Science / Physics / Mathematical & Computational |
| Export Citation | BiBTeX EndNote RefMan |