  In this paper, we study the initial-boundary value problem for a
pseudo-parabolic equation in magnetic fractional Orlicz-Sobolev spaces. First,
by employing the imbedding theorems, the theory of potential wells and the
Galerkin method, we prove the existence and uniqueness of global solutions with
subcritical initial energy, critical initial energy and supercritical initial
energy, respectively. Furthermore, we prove the decay estimate of global
solutions with sub-sharp-critical initial energy, sharp-critical initial energy
and supercritical initial energy, respectively. Specifically, we need to
analyze the properties of $\omega$-limits of solutions for supercritical
initial energy. Next, we establish the finite time blowup of solutions with
sub-sharp-critical initial energy and sharp-critical initial energy,
respectively. Finally, we discuss the convergence relationship between the
global solutions of the evolution problem and the ground state solutions of the
corresponding stationary problem.
