Global existence and nonexistence analyses for a magnetic fractional pseudo-parabolic equation

Abstract

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.