  Dynamical systems and physical models defined on idealized continuous phase
spaces are known to exhibit non-computable phenomena, examples include the wave
equation, recurrent neural networks, or Julia sets in holomorphic dynamics.
Inspired by the works of Moore and Siegelmann, we show that ideal fluids,
modeled by the Euler equations, are capable of simulating poly-time Turing
machines with polynomial advice on compact three-dimensional domains. The
complexity class that is shown to be computable by stationary ideal fluids is
precisely the one considered by Siegelmann in her study of analog recurrent
neural networks: the class $P/poly$. In the last part, we introduce a new class
of symbolic systems, related to countably piecewise linear transformations of
the unit square, that is capable of simulating Turing machines with advice in
real-time, contrary to previously known models.
