Dalia Fishelov,Jean-Pierre Croisille,Matania Ben-Artzi

Navier-Stokes Equations in Planar Domains

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This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.
A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.
This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics.
Contents:Basic Theory:IntroductionExistence and Uniqueness of Smooth SolutionsEstimates for Smooth SolutionsExtension of the Solution OperatorMeasures as Initial DataAsymptotic Behavior for Large TimeSome Theorems from Functional AnalysisApproximate Solutions:IntroductionNotationFinite Difference Approximation to Second-Order Boundary-Value ProblemsFrom Hermitian Derivative to the Compact Discrete Biharmonic OperatorPolynomial Approach to the Discrete Biharmonic OperatorCompact Approximation of the Navier–Stokes Equations in Streamfunction FormulationFully Discrete Approximation of the Navier–Stokes EquationsNumerical Simulations of the Driven Cavity ProblemReadership: Graduate students and researchers in applied mathematics (particularly computational fluid dynamics), partial differential equations, and mathematical physics (specifically nonlinear evolution equations).
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3,885 printed pages
Original publication


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