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  • 1
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    Vortex Methods in Two-Dimensional Fluid Dynamics (1984)
    Berlin ; Heidelberg : Springer
    Details
    Keywords: Vortex ; fluid dynamics ; Euler equations ; Navier-Stokes equations
    Description / Table of Contents: Pages 1-3: Introduction --- Pages 4-11: Euler equations --- Pages 12-32: Vortex model --- Pages 33-52: An existence theorem for Euler equations --- Pages 53-66: Further considerations on vortex model --- Pages 67-79: A mean field limit --- Pages 80-86: Navier-Stokes equations --- Pages 87-98: Diffusion process and Navier-Stokes equations --- Pages 99-115: Mean field limit and propagation of chaos for Navier-Stokes equations --- Pages 116-129: The problem of boundary conditions, chorin method and concluding remarks
    Pages: Online-Ressource (III, 141 Seiten) , 4 schwarz-weiß Abbildungen
    ISBN: 9783540133520
    URL: http://www.springerlink.com/openurl.asp?genre=book&isbn=978-3-540-13352-0
    Language: English
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    E-BOOK
  • 2
    Electronic Resource
    Electronic Resource
    On the vortex flow in bounded domains (1982)
    Springer
    Communications in mathematical physics 85 (1982), S. 265-273 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the motion ofN vortices in bounded domains in IR2. We prove that the set of initial positions which lead to a collapse of two or more vortices has Lebesgue measure zero. We extend this result to the stochastic motion of the vortices, where the stochasticity comes from a Wiener-noise term, which is added to the deterministic equation of motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01254459
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  • 3
    Electronic Resource
    Electronic Resource
    Generation of vorticity near the boundary in planar Navier-Stokes flows (1984)
    Springer
    Communications in mathematical physics 96 (1984), S. 59-95 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct the solutions of the planar Navier-Stokes flow for a viscous incompressible fluid in the half-plane, by means of a boundary layer equation describing the production of vorticity on the boundary. Regularity properties are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217348
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear stability of circular vortex patches (1985)
    Springer
    Communications in mathematical physics 99 (1985), S. 435-450 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper proves that circular vortex patches in the plane are stable for the nonlinear dynamical system generated by the Euler equations of incompressible fluids. This is achieved by establishing a relative variational principle in terms of either energy or angular momentum. Thus, we exploit and extend Arnold's idea in (1965, 1969) to a nonsmooth setting as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01240356
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  • 5
    Electronic Resource
    Electronic Resource
    Hydrodynamics in two dimensions and vortex theory (1982)
    Springer
    Communications in mathematical physics 84 (1982), S. 483-503 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the Navier-Stokes equation for a viscous and incompressible fluid inR 2. We show that such an equation may be interpreted as a mean field equation (Vlasov-like limit) for a system of particles, called vortices, interacting via a logarithmic potential, on which, in addition, a stochastic perturbation is acting. More precisely we prove that the solutions of the Navier-Stokes equation may be approximated, in a suitable way, by finite dimensional diffusion processes with the diffusion constant related to the viscosity. As a particular case, when the diffusion constant is zero, the finite dimensional theory reduces to the usual deterministic vortex theory, and the limiting equation reduces to the Euler equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01209630
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  • 6
    Electronic Resource
    Electronic Resource
    Convergence of Galerkin approximation for two-dimensional Vlasov-Poisson equation (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 790-801 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammmenfassung Wir geben eine explizite Abschätzung der Konvergenzgeschwindigkeit einer endlichdimensionalen Fourier-Hermite-Entwicklung gegen die Lösung der Vlasov-Poisson-Gleichung für den räumlich 2-dimensionalen periodischen Fall an.
    Notes: Abstract We give explicit estimates on the rate of convergence of the solutions of finite dimensional truncations (by means of Fourier-Hermite expansion) of Vlasov-Poisson equation in a two-dimensional flat torus.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945444
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  • 7
    Electronic Resource
    Electronic Resource
    On the statistical solutions of Vlasov-Poisson equations in two dimensions (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 508-519 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wir untersuchen die Frage nach der Eindeutigkeit statistischer Lösungen der Vlasov-Poisson-Gleichung für eln Eiektronenplasma im räumlich zweidimensionalen periodischen Fall.
    Notes: Abstract We investigate the problem of the uniqueness of the statistical solutions of the Vlasov-Poisson equations for an electron plasma in a two dimensional torus.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945293
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  • 8
    Electronic Resource
    Electronic Resource
    Euler evolution for singular initial data and vortex theory (1983)
    Springer
    Communications in mathematical physics 91 (1983), S. 563-572 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the evolution of a two dimensional, incompressible, ideal fluid in a case in which the vorticity is concentrated in small, disjoint regions of the physical space. We prove, for short times, a connection between this evolution and the vortex model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01206023
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  • 9
    Electronic Resource
    Electronic Resource
    The Boltzmann equation for weakly inhomogeneous data (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 393-407 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We solve the initial value problem associated to the nonlinear Boltzmann equation in the case in which the initial distribution has sufficiently small spatial gradients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238905
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  • 10
    Electronic Resource
    Electronic Resource
    Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum (1987)
    Springer
    Communications in mathematical physics 113 (1987), S. 79-85 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a system ofN hard spheres in the Boltzmann-Grad limit (i.e.d→0,N→∞,Nd 2→λ−1〉0, whered is the diameter of the spheres). If λ is sufficiently large, and if the joint distribution densities factorize at time zero, with the one particle distribution decaying sufficiently rapidly in space and velocities, we prove that the time evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum. This result improves and is based on a previous paper [1], valid only in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221398
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