A sufficient condition for the existence of smooth solutions of the relativistic cold plasma equations on any given time interval

In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such sufficient conditions take into account the smallness properties of not only the derivatives of the initial data but also the initial data themselves. The accuracy of the obtained initial condition is investigated using a numerical experiment. The structure of the emerging singularities is also studied.