Extended crystal PDE's stability.II: The extended crystal MHD-PDE's

This paper is the second part of a work devoted to the algebraic topological characterization of PDE's stability and its relation with an important class of PDE's called {\em extended crystals PDE's}. In fact, their integral bordism groups can be considered extensions of subgroups of crystallographic groups. This allows us to identify a characteristic class that measures the obstruction to the existence of global solutions. In part I we identified criteria to recognize PDE's that are stable (in extended Ulam sense) and in their regular smooth solutions do not occur finite time unstabilities, ({\em stable extended crystal PDE's}). Here we study in some details a new PDE encoding anisotropic incompressible magnetohydrodynamics. A stable extended crystal MHD-PDE's is obtained where in its smooth solutions do not occurr unstabilities in finite times. These results are considered first for systems without body energy source and after by introducing also a contribution by energy source in order to take into account of nuclear energy production. A condition in order solutions satisfy the second principle of thermodynamics is given.