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  • 非线性偏微分方程分析讲义(第3卷)(英文)[精装]
  • 共3个商家     66.80元~75.60
  • 作者:林芳华(编者),张平(编者)
  • 出版社:高等教育出版社;第1版(2013年1月1日)
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  • ISBN:9787040363395

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    《非线性偏微分方程分析讲义(第3卷)(英文)》可作为从事非线性偏微分方程、特别是流体力学方程和微局部分析研究的科研人员和教师的学习和参考用书。

    目录

    T.Alazard,N.Burq,and C.Zuily:Low Regularity Cauchy Theory for the Water-waves Problem:Canals and Wave Pools
    Jean-Yves Chemin:Navier-Stokes System
    Isabelle Gallagher:Semi-classical Analysis of Oceanic Flows
    Patrick Gérard:An Introduction to the Cubic Szeg(o) Equation
    David Gérard-Varet:Some Recent Mathematical Results on Fluid-Solid Interaction
    Hideo Kozono and Taku Yanagisawa:Lr-Helmholtz Decomposition and Its Application to the Navier-Stokes Equations
    F.Rousset and N.Tzvetkov:Lectures on Transverse Instability of Solitary Water-waves
    J.-C.Saut:Lectures on the Mathematical Theory of Viscoelastic Fluids

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    3.2 Domains with boundaries: the boundary layer
    When the Navier-Stokes solutions uε and the Euler solution u are defined in a domain Ω with boundaries,the convergence issue gets considerably harder.The difficulty lies in the boundary conditions that are added at δΩ.For ε=Ω(Euler equation),only the tangency condition
    u·nδΩ=0 (3.2)
    is satisfied.But for ε≠0,that is when the viscosity is turned on,the fluid must stick at the boundary,which translates into the Dirichlet condition
    uε|δΩ= 0.(3.3)
    In order to satisfy this no-slip condition,the tangential momentum at the boundary is somehow diffused into the domain.As the viscosity is very small,this change of momentum is concentrated near the boundary,in a thin zone called a boundary layer.Mathematically,this boundary layer corresponds to a singular dependence of uε with respect to ε.Hence,the whole point is to understand this boundary layer and its impact on the asymptotics ε→0.
    One can even be more specific: the whole point is to determine wether or not the velocity field uε concentrates in an e-neighborhood of the boundary.