Quasilinear hyperbolic Fuchsian systems and AVTD behavior in   T2-symmetric vacuum spacetimes
  We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply this theory in order to show the existence of smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein equations, which exhibit AVTD (asymptotically velocity term dominated) behavior in the neighborhood of their singularities and are polarized or half-polarized. 
Ellery Ames, Florian Beyer, James Isenberg, and Philippe G. LeFloch
gr-qc