A class of large solutions to the 3D incompressible MHD and Euler equations with damping

In this paper, we derive the global existence of smooth solutions of the 3D incompressible Euler equations with damping for a class of large initial data, whose Sobolev norms H ^s can be arbitrarily large for any s ≥ 0. The approach is through studying the quantity representing the difference between the vorticity and velocity. And also, we construct a family of large solutions for MHD equations with damping.