Singularity formation in a class of stretched solutions of the equations for ideal magneto-hydrodynamics
Singularity formation in a class of stretched solutions of the equations for ideal magneto-hydrodynamics
A class of stretched solutions of the equations for three-dimensional, incompressible, ideal magneto-hydrodynamics (MHD) is studied. In Elsasser variables, VĀ± = UĀ±B, these solutions have the form VĀ± = (vĀ±, v3Ā±) where vĀ± = vĀ±(x,y,t) and v3Ā±(x,y,z,t) = zĪ³Ā±(x,y,t) + Ī²Ā±(x,y,t). Two-dimensional partial differential equations for Ī³Ā±, vĀ± and Ī²Ā± ā¦