  We give a direct construction of invariant measures and global flows for the
stochastic quantization equation to the quantum field theoretical $\Phi
^4_3$-model on the $3$-dimensional torus. This stochastic equation belongs to a
class of singular stochastic partial differential equations (SPDEs) presently
intensively studied, especially after Hairer's groundbreaking work on
regularity structures. Our direct construction exhibits invariant measures and
flows as limits of the (unique) invariant measures for corresponding finite
dimensional approximation equations. Our work is done in the setting of
distributional Besov spaces, adapting semigroup techniques for solving
nonlinear dissipative parabolic equations on such spaces and using methods that
originated from work by Gubinelli et al on paracontrolled distributions for
singular SPDEs.
