The Limit Of The Vanishing Viscosity For The Incompressible 3D MHD Equations With Helical Symmetry

In this paper?we are concerned with the vanishing viscosity problem for the three-dimensional MHD equations with helical symmetry,in the whole space.We let(u0v,b0v)be divergence free and helical vector fields.We prove the global existence of weak helical solutions provided the initial velocity belongs to L2 and is helically symmetric;If initial data belongs to Hper 1,by energy estimates,we will prove the regularity of solutions can be improved,then the MHD equatins have a unique and global strong solution which is helically symmetric.In the process of proving the vanishing limit of viscosity,to overcome the difficulty of vorticity stretching terms,we utilize a decomposition of helical vector fields to obtain the required a priori estimates:u=U+??/|?|2,Therefore,we get the uniform bound about the curl of the velocity and the magnetic field.Using Aubin-Lions compactness theorem and diagonal argument to(uv,bv)?(u0;b0)strongly in L2(0,T;Lloc2(D)).