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We set up the singular initial value problem for quasilinear hyperbolicFuchsian systems of first order and establish an existence and uniquenesstheory for this problem with smooth data and smooth coefficients (and with evenlower regularity). We apply this theory in order to show the existence ofsmooth (generally not analytic) T2-symmetric solutions to the vacuum Einsteinequations, which exhibit AVTD (asymptotically velocity term dominated) behaviorin the neighborhood of their singularities and are polarized or half-polarized.

Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes