Thursday, December 13, 2012

1212.2867 (Demetrios Christodoulou et al.)

Compressible Flow and Euler's Equations    [PDF]

Demetrios Christodoulou, Shuang Miao
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. We obtain a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there.
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