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Existence theorem in the variational problem for compressible inviscid fluids. (English) Zbl 0658.76065

This paper starts from Young’s concept of a generalized curve, which may be used if the existence of minima of hemibounded functionals with a non- convex integrand are considered in the context of functions whose curvature is uniformly bounded. The author then proceeds to modify this approach in an attempt to define a weak solution for the equations of an inviscid compressible fluid on the basis of a variational principle.
Reviewer: A.Jeffrey

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
49S05 Variational principles of physics
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References:

[1] DI PERNA.R.: Generalized solutions to conservation laws. Systems of nonlinear partial differential equations, Ball, J.M. (ed.) NATO ASI Seris, C.Reidel Publishing Col.305–309 (1983)
[2] GUZMAN,M.: Differentiation of integrals in Rn. Zetcutre notes in Math.Berlin-Heidelberg-New York. Springer-Verlag. 1975
[3] SERRIN,J.: Mathematical Principles of Classical Fluid Dynamics. Encyclopedia of Physics, vol.13, 1, Springer-Verlag, 1959
[4] SHELUKHIN, V.V.: On one class of Young generalized solutions to equations of inviscouse complessible fluid. Din. Sploshnoi Sredy. vol.80, 160–163. (1987) (in Russian) · Zbl 0666.76091
[5] TARTAR, L.: Compensated compacteness and applications to partial differential equations. Research Notes in Math. Heriot-Watt Symposium, vol. 4, Knops. R.J., (ed.) New-York; Pitman Press, p.136–212 (1979)
[6] WEYL, H.: Shock waves in arbitrary fluids. Communs. Pure Appl. Math., 2, 103–122, (1949) · Zbl 0035.42004 · doi:10.1002/cpa.3160020201
[7] YOSHIDA, K.: Functional Analysis, Berlin-Heidelberg-New York, Springer, 1978
[8] YOUNG, L.C.: Lectures on the calculus of variations and optical control theory. Philadelphia-Landon, W.B. Saunders, Co. 1969 · Zbl 0177.37801
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