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Formation of singularities in three-dimensional compressible fluids

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Abstract

Presented are several results on the formation of singularities in solutions to the three-dimensional Euler equations for a polytropic, ideal fluid under various assumptions on the initial data. In particular, it is shown that a localized fluid which is initially compressed and outgoing, on average, will develop singularities regardless of the size of the initial disturbance.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 93106, Santa Barbara, California, USA

    Thomas C. Sideris

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  1. Thomas C. Sideris
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Communicated by L. Nirenberg

Research supported in part by the National Science Foundation

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Sideris, T.C. Formation of singularities in three-dimensional compressible fluids. Commun.Math. Phys. 101, 475–485 (1985). https://doi.org/10.1007/BF01210741

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  • DOI: https://doi.org/10.1007/BF01210741

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