Article

# Line Solutions for the Euler and Euler-Poisson Equations with Multiple Gamma Law

05/2010; DOI:abs/1005.3651
Source: arXiv

ABSTRACT In this paper, we study the Euler and Euler-Poisson equations in $R^{N}$,
with multiple $\gamma$-law for pressure function:
P(\rho)=e^{s}\sum_{j=1}^{m}\rho^{\gamma_{j}}, where all
$\gamma_{i+1}>\gamma_{i}\geq1$, is the constants. The analytical line solutions
are constructed for the systems. It is novel to discover the analytical
solutions to handle the systems with mixed pressure function. And our solutions
can be extended to the systems with the generalized multiple damping and
pressure function.

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### Keywords

analytical line solutions

Euler-Poisson equations

generalized multiple damping

mixed pressure function

multiple $\gamma$-law

pressure function

solutions

systems