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The Leray problem for 2D inhomogeneous fluids

Volume 70 / 2005

Farid Ammar-Khodja, Marcelo M. Santos Banach Center Publications 70 (2005), 51-59 MSC: 35Q30, 76D05. DOI: 10.4064/bc70-0-3

Abstract

We formulate the Leray problem for inhomogeneous fluids in two dimensions and outline the proof of the existence of a solution. There are two kinds of results depending on whether the given value for the density is a continuous function or only an $L^\infty$ function. In the former case, the given densities are attained in the sense of uniform convergence and in the latter with respect to weak-$\ast$ convergence.

Authors

  • Farid Ammar-KhodjaDépartement de Mathématiques & UMR 6623, Université de Franche-Comté
    16, route de Gray, 25030 Besançon Cedex, France
    e-mail
  • Marcelo M. SantosDepartamento de Matemática, IMECC–UNICAMP
    Cx. Postal 6065, 13.081-970 Campinas, SP, Brazil
    e-mail

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