Global existence of smooth solutions for the magnetic Schrödinger equation arising from hot plasma

We consider a type of dispersive–dissipative system that arises in the infinite ion acoustic speed limit of the magnetic Zakharov system in a hot plasma. It is shown that this system admits a unique global smooth solution for suitably small initial data. Decay estimates for the solution are also obtained. In particular, the L2L2 and L∞L∞ decay rates for the magnetic field are sharp.