Transition from a kinetic to a hydrodynamic model of cold plasma: issues of smoothness of the solution

Abstract

Using the simplest one-dimensional example, we analyze the transition from the kinetic model of cold plasma (Landau, Iordansky) to the hydrodynamic model. During the transition, the class of initial Cauchy data corresponding to a globally smooth solution is narrowed. We construct moment chains that satisfy similar first-order equations and offer an explanation of why cutting them off at each next step expands the class of initial data corresponding to a smooth solution.