The pressureless Euler equations can be used as simple models of cosmology or plasma physics .
In this paper , we construct the exact solutions in non-radial symmetry to the pressureless Euler equations in R ^ { N } :

\left \ { \begin { array } [ c ] { c } \rho ( t, \vec { x } ) = \frac { f \left ( \frac { 1 } { a ( t ) ^ { s } } % \underset { i = 1 } { \overset { N } { \sum } } x _ { i } ^ { s } \right ) } { a ( t ) ^ { N } } \text { , } \vec { u } ( t% , \vec { x } ) = \frac { \overset { \cdot } { a } ( t ) } { a ( t ) } \vec { x } ,\ a ( t ) = a _ { 1 } + a _ { 2 } t, \end { array } \right . where the arbitrary function f \geq 0 and f \in C ^ { 1 } ; s \geq 1 , a _ { 1 } > 0 and a _ { 2 } are constants . In particular , for a _ { 2 } < 0 , the solutions blow up on the finite time T = - a _ { 1 } / a _ { 2 } .

Moreover , the functions ( 1 ) are also the solutions to the pressureless Navier-Stokes equations .

Key Words : Pressureless Gas , Euler Equations , Exact Solutions , Non-Radial Symmetry , Navier-Stokes Equations , Blowup , Free Boundary