  We establish the existence of a stable family of solutions to the Euler
equations on Kasner backgrounds near the singularity with the full expected
asymptotic data degrees of freedom and no symmetry or isotropy restrictions.
Existence is achieved through transforming the Euler equations into the form of
a symmetric hyperbolic Fuchsian system followed by an application of a new
existence theory for the singular initial value problem. Stability is shown to
follow from the existence theory for the (regular) global initial value problem
for Fuchsian systems that was developed in arXiv:1907.04071. In fact, for each
solution in the family, we prove the existence of an open set of nearby
solutions with the same qualitative asymptotics and show that any such
perturbed solution agrees again with another solution of the singular initial
value problem. All our results hold in the regime where the speed of sound of
the fluid is large in comparison to all Kasner exponents. This is interpreted
as the regime of stable fluid asymptotics near Kasner big bang singularities.
