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Ill-posed Cauchy problems for ideal gas equations and their regularization. (English) Zbl 0641.76068

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 19, 17 p. (1987).
The author defines the degree of incorrectness of a problem concerning suitable initial perturbations. This property is equivalent with the discontinuity of the solutions with respect to some topology. The author determines this degree for the system “S” of equations governing flows of ideal barotropic gases. To solve incorrect problems, the author applies regularizations. Regularization of a sequence of solutions consists in the calculation of the limit in the sense of distributions. This is carried out for the system “S”. The author also considers regularizations for the Navier-Stokes equations for compressible fluids and for the inverse heat equation.
Reviewer: E.Adams

MSC:

76N15 Gas dynamics (general theory)
35R25 Ill-posed problems for PDEs
35Q30 Navier-Stokes equations
Full Text: Numdam EuDML