Magneto‐hydrodynamic equations and parametric flag microlocal quantities at binary time interval

In this paper, we establish the well‐posedness of the Cauchy problem for incompressible magneto‐hydrodynamic equations by using parametric Meyer wavelets. The velocity field and magnetic field are expanded according to parametric wavelets given by a discrete set of thresholds. The evolution of these two types of fields is described by the relationship of parameterized flag microlocal quantities over binary time intervals. The corresponding iteration space is defined by the decay of the single norm, and the single norm is defined by the parametric flag microlocal quantities at a set of binary time interval.