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Formation of singularities in three-dimensional compressible fluids

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

   Thomas C. Sideris

1. Thomas C. Sideris

Communicated by L. Nirenberg

Research supported in part by the National Science Foundation

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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• Received: 10 September 1983

• Revised: 11 March 1985

• Issue Date: December 1985

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

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