Formation of singularities for a linearly degenerate hyperbolic system arising in magnetohydrodynamics

This article is concerned with the singularity formation of smooth solutions for a nonhomogeneous hyperbolic system arising in magnetohydrodynamics. The system owns four linearly degenerate characteristic fields that influence each other in the relations of second derivatives, making the problem difficult to handle. We develop the characteristic decomposition technique to apply the nonlinear hyperbolic equations with more than two wave characteristics. It is verified that the smooth solution can form a singularity in finite time and the density itself tends to infinity at the blowup point for a special kind of initial data.