On the regular solutions for a generalized compressible Landau–Lifshitz–Bloch equation

In this paper, first we will prove that the regular solution for the compressible Landau–Lifshitz–Bloch equation found in (Ayouch, C., Benmouane, M. & Essoufi, E. H. Regular solution for the compressible Landau–Lifshitz–Bloch equation in a bounded domain of \(\mathbb {R}^{3}\) ${\mathbb{R}}^3$ . J Elliptic Parabol Equ 8, 419-441 (2022)) is global in time in dimension two when the initial data is small enough. Next, we deal with a two generalized version of the compressible LLB equation and we prove existence and uniqueness of regular solution for this new models.