A connection between viscous profiles and singular ODEs

@misc{citeulike:2309954, abstract = {We are concerned with the viscous profiles for a class of mixed hyperbolic parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form \$V' = f (V) / z (V) + g (V).\$ Here \$V \in R^N\$ and the functions f and g take values into \$R^N\$ and are smooth. The real valued function z is as well regular: the equation is singular in the sense that z(V) can attain the value 0.}, author = {Bianchini, Stefano and Spinolo, Laura V. }, citeulike-article-id = {2309954}, eprint = {0801.4532}, keywords = {1d, navier-stokes, viscosity-solution}, month = {Jan}, posted-at = {2008-01-31 08:41:15}, priority = {2}, title = {A connection between viscous profiles and singular ODEs}, url = {http://arxiv.org/abs/0801.4532}, year = {2008} }

TY - ELEC ID - citeulike:2309954 L3 - citeulike-article-id:2309954 TI - A connection between viscous profiles and singular ODEs N2 - We are concerned with the viscous profiles for a class of mixed hyperbolic parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $V' = f (V) / z (V) + g (V).$ Here $V \in R^N$ and the functions f and g take values into $R^N$ and are smooth. The real valued function z is as well regular: the equation is singular in the sense that z(V) can attain the value 0. KW - 1d KW - navier-stokes KW - viscosity-solution AU - Bianchini, Stefano AU - Spinolo, Laura PY - 2008/Jan/29/ UR - http://arxiv.org/abs/0801.4532 ER -