{"product_id":"9781783263011","title":"Navier-stokes Equations In Planar Domains","description":"\u003cp\u003eThis 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”.\u003c\/p\u003e\u003cp\u003eA 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.\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eBasic Theory:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eExistence and Uniqueness of Smooth Solutions\u003c\/li\u003e\n\u003cli\u003eEstimates for Smooth Solutions\u003c\/li\u003e\n\u003cli\u003eExtension of the Solution Operator\u003c\/li\u003e\n\u003cli\u003eMeasures as Initial Data\u003c\/li\u003e\n\u003cli\u003eAsymptotic Behavior for Large Time\u003c\/li\u003e\n\u003cli\u003eSome Theorems from Functional Analysis\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eApproximate Solutions:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eNotation\u003c\/li\u003e\n\u003cli\u003eFinite Difference Approximation to Second-Order Boundary-Value Problems\u003c\/li\u003e\n\u003cli\u003eFrom Hermitian Derivative to the Compact Discrete Biharmonic Operator\u003c\/li\u003e\n\u003cli\u003ePolynomial Approach to the Discrete Biharmonic Operator\u003c\/li\u003e\n\u003cli\u003eCompact Approximation of the Navier–Stokes Equations in Streamfunction Formulation\u003c\/li\u003e\n\u003cli\u003eFully Discrete Approximation of the Navier–Stokes Equations\u003c\/li\u003e\n\u003cli\u003eNumerical Simulations of the Driven Cavity Problem\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers in applied mathematics (particularly computational fluid dynamics), partial differential equations, and mathematical physics (specifically nonlinear evolution equations).\u003cbr\u003e","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":47136966836464,"sku":"9781783263011","price":39.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781783263011_p0.jpg?v=1763722689","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781783263011","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}