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Multidimensional Hyperbolic Problems and Computations pp 23–37Cite as

The Approximation of Weak Solutions to the 2-D Euler Equations by Vortex Elements

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 29))

Abstract

It is shown that the Euler equations of two-dimensional incompressible flow, with initial vorticity in L p, p > 1, possess weak solutions which may be obtained as a limit of vortex “blobs”; i.e., the vorticity is approximated by a finite sum of cores of prescribed shape which are advected according to the corresponding velocity field. If the vorticity is instead a finite measure of bounded support, such approximations lead to a measure-valued solution of the Euler equations in the sense of DiPerna and Majda [7]. The analysis is closely related to that of [7].

Research supported by D.A.R.P.A. Grant N00014-86-K-0759 and N.S.F. Grant. DMS-8800347.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27706, USA

    J. Thomas Beale

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  1. J. Thomas Beale
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Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY, 11794-3600, USA

    James Glimm

  2. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Andrew J. Majda

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© 1991 Springer-Verlag New York, Inc.

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Beale, J.T. (1991). The Approximation of Weak Solutions to the 2-D Euler Equations by Vortex Elements. In: Glimm, J., Majda, A.J. (eds) Multidimensional Hyperbolic Problems and Computations. The IMA Volumes in Mathematics and Its Applications, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9121-0_3

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  • DOI: https://doi.org/10.1007/978-1-4613-9121-0_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9123-4

  • Online ISBN: 978-1-4613-9121-0

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