Formation of singularities in compressible fluids in two-space dimensions

Rammaha, M. A.

doi:10.1090/S0002-9939-1989-0984811-5

Formation of singularities in compressible fluids in two-space dimensions
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Proc. Amer. Math. Soc. 107 (1989), 705-714 Request permission

Abstract:

Classical solutions to the two-dimensional Euler equations for a polytropic ideal fluid are considered. It is shown that any local ${C^1}$-flow, regardless of the size of the initial disturbance, will develop singularities in finite-time provided the front of the initial disturbance satisfies certain conditions.

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