Sideris, Thomas C. Formation of singularities in three-dimensional compressible fluids. (English) Zbl 0606.76088 Commun. Math. Phys. 101, 475-485 (1985). The author studies the formation of singularities in solutions to the initial value problem for the three dimensional compressible Euler equations for polytropic, ideal fluids. It is shown that under certain conditions smooth solutions develope singularities, even for small initial data. Reviewer: G.Warnecke Cited in 8 ReviewsCited in 244 Documents MSC: 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35L65 Hyperbolic conservation laws 35L60 First-order nonlinear hyperbolic equations Keywords:formation of singularities; initial value problem; compressible Euler equations; polytropic, ideal fluids; smooth solutions PDF BibTeX XML Cite \textit{T. C. Sideris}, Commun. Math. Phys. 101, 475--485 (1985; Zbl 0606.76088) Full Text: DOI References: [1] Courant, R., Friedrichs, K. O.: Supersonic flow and shock waves. New York: Interscience 1948 · Zbl 0041.11302 [2] John, F.: Formation of singularities in one-dimensional nonlinear wave propagation. Commun. Pure Appl. Math.27, 377-405 (1974) · Zbl 0302.35064 [3] John, F.: Blow-up of radial solutions ofu tt =C 2(u t )?u in three space dimensions. To appear [4] Kato, T.: The Cauchy problem for quasilinear symmetric systems. Arch. Ration. Mech. Anal.58, 181-205 (1975) · Zbl 0343.35056 [5] Klainerman, S. Majda, A.: Formation of singularities for wave equations including the nonlinear vibrating string. Commun. Pure Appl. Math.33, 241-263 (1980) · Zbl 0443.35040 [6] Klainerman, S. Majda, A.: Compressible and incompressible fluids. Commun. Pure Appl. Math.35, 629-651 (1982) · Zbl 0489.76081 [7] Lax, P.: Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys.5, 611-613 (1964) · Zbl 0135.15101 [8] Liu, T.-P.: The development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations. J. Differ. Equations33, 92-111 (1979) · Zbl 0404.35071 [9] Sideris, T.: Global behavior of solutions to nonlinear wave equations in three space dimensions. Commun. Partial Differ. Equations8, 12, 1291-1323 (1983) · Zbl 0534.35069 [10] Sideris, T.: Formation of singularities of solutions to nonlinear hyperbolic equations. Arch. Ration. Mech. Anal.86, 4, 369-381 (1984) · Zbl 0564.35070 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.