Finite-energy spacetimes with torus symmetry. Cauchy stability of Einstein-Euler and Einstein-Navier-Stokes areal flows

We establish finite-energy Cauchy stability for vacuum and matter spacetimes with $T^2$ symmetry on $T^3$, under general constitutive equations satisfying hyperbolicity and mild asymptotic conditions at vacuum and large mass-energy density. First, using the area of the symmetry orbits as a time func