| Abstract: | We study a system of equations consisting of the two-dimensional Bürgers equation and the continuity equation. In 1970 such
a system was proposed by Ya. B. Zeldovich for describing the formation of the large-scale structure of the Universe. In the
present paper, for the divergent form of this system (the zero-pressure gas dynamics system), we rigorously define the notion
of its generalized solution (in the sense of distributions) in terms of Radon measures and obtain a generalization of the
Rankine-Hugoniot relations. By using these relations, we show that, in general, the variational representation of generalized
solutions valid for the one-dimensional system of zero-pressure gas dynamics does not make sense in the two-dimensional case.
Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 760–769, November, 1999. |
