Protoplanetary discs are made of gas and dust orbiting a young star. They also the birth place planetary systems, which motivates large amount observational theoretical research. In these lecture notes, I present review magnetic mechanisms applied to outer regions ( $R\gtrsim 1\ \mathrm {AU}$ ) discs, planet-formation regions. contrast usual astrophysical plasmas, in is noticeably cold $T < ...

We prove the global regularity of the solution pair to the Ndimensional logarithmically supercritical magnetohydrodynamics system with zero diffusivity. This is the endpoint case omitted in the work of [24]; it also improves some previous results logarithmically.

We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is discussed.