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A tiny step towards a theory of functional derivative equations —A strong solution of the space-time hopf equation

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The Navier-Stokes Equations II — Theory and Numerical Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1530))

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Abstract

In this note, we construct a strong solution of the space-time Hopf equation,

$$(\frac{\partial }{{\partial t}} - v\Delta )\frac{{\delta Z(\eta )}}{{\delta \eta _\ell (x,t)}} = i\left[ {\tilde T^* \left\{ {\frac{{\delta ^2 Z(\eta )}}{{\delta \eta _j (x,t)\delta \eta _k (x,t)}}} \right\}} \right]^\ell + if^\ell (x,t)Z(\eta )$$

with certain subsidary conditions, which is an example of functional derivative equations and is manageable using a tiny part of “analysis in functional spaces”.

This paper is in final form and no similar paper has been or is being submitted elsewhere.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, Japan

    Atsushi Inoue

Authors
  1. Atsushi Inoue
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Editor information

John G. Heywood Kyûya Masuda Reimund Rautmann Vsevolod A. Solonnikov

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Dedicated to Prof.Nobuyuki IKEDA for his retirement

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© 1992 Springer-Verlag

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Inoue, A. (1992). A tiny step towards a theory of functional derivative equations —A strong solution of the space-time hopf equation. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations II — Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090346

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  • DOI: https://doi.org/10.1007/BFb0090346

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56261-0

  • Online ISBN: 978-3-540-47498-2

  • eBook Packages: Springer Book Archive

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