Blow-up of three-dimensional isentropic compressible magnetohydrodynamics equations

Under the conditions that the gradient of the velocity and magnetic field satisfy a certain decay, and the initial total momentum does not vanish, the explosion phenomenon of classical solutions of the three-dimensional isentropic compressible magnetohydrodynamic equation in finite time is studied. Blow-up result is derived by constructing the sphere to prove the conservation of mass, momentum and energy in full space and applying Hölder inequality, interpolation inequalities, and other methods to deal with relevant nonlinear terms.