ABSTRACT

In this talk, we present the global well-posedness of a tri-dimensional MHD system with only vertical viscosity in velocity equation for the large axisymmetric initial data. By making good use of the axisymmetric structure of flow and the maximal smoothing effect of vertical diffusion, we show that sup_2<=p<∞∫₀^t(("||δ_zu(Τ)||²_L^p)/p^3/4)dΤ<∞. with this regularity for the vertical first derivative of velocity vector field, we further establish losing estimates for the anisotropy tri-dimensional MHD system to get the high regularity of (u, b), which guarantees that ∫₀^t||∇u(Τ)||_L∞dΤ<∞. This together with the classical commutator estimate entails the global regularity of the solution.

[Light refreshments will be served outside the venue at 4:50-5:10 pm. Please come and join us.]