| Abstract: |
| We investigate the gradient blow-up mechanism of classical solution to the initial value problem of radially symmetric MHD equations in two spatial dimensions, where the inhomogeneity caused by polar radius brings new difficulties in the high-dimensional problem. By developing delicate estimates for the Riemann variables with coupling effects introduced by the magnetic field, we first obtain the upper bound for the solution itself under compressive initial conditions. Furthermore, we also get the blow-up of first derivatives of solution by constructing the Riccati equations. This generalizes the result of G. Chen, R. Young and Q. Zhang`s work for 1-D MHD with orthogonal magnetic field [J. Hyperbolic Differ. Equ. 10 (2013), 149-172]. |
|