Development of Studies of the School of L.I. Sedov at the Chair of Hydromechanics

An overview of recent works in the field of gas dynamics and plasma dynamics, which were initiated by academician L.I. Sedov and his followers, is given. An analytical study of the equations was carried out, exact solutions were constructed and the problem of energy–momentum concentration was solved. Higher invariants of characteristics for a system of equations of one-dimensional gas dynamics in Eulerian and Lagrangian variables for special adiabatic exponents are found. Based on the use of higher invariants of characteristics, the solution of the Cauchy problem is reduced to a system of ordinary differential equations. Two Cauchy problems are presented, the solutions of which exist indefinitely without a gradient catastrophe.