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- W122397573 abstract "We derive an explicit formula for global weak solutions of the one dimensional system of pressure-less Euler-Poisson equations. Our variational formulation is an extension of the well-known formula for entropy solutions of the scalar inviscid Burgers' equation: since the characteristics of the Euler-Poisson equations are parabolas, the representation of their weak solution takes the form of a quadratic version of the celebrated Lax-Oleinik variational formula. Three cases are considered. (i) The variational formula recovers the solution in the attractive case; (ii) It represents a repulsive solution which is different than the one obtained by the sticky particle construction; and (iii) the result is further extended to the multi-dimensional Euler-Poisson system with radial symmetry." @default.
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- W122397573 date "2011-02-28" @default.
- W122397573 modified "2023-09-27" @default.
- W122397573 title "A variational representation of weak solutions for the pressureless Euler-Poisson equations" @default.
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