Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations: I. Green formulas

Three nonlinear equations for ion acoustic and drift waves in a plasma are derived. The fundamental solution of the common linear part of the resulting nonlinear equations is constructed, and its smoothness properties are studied. Next, the second Green formula in a bounded domain is constructed, which is then used to derive the third Green formula in a bounded domain. Finally, two variants of the third Green formula in the entire space are constructed in a certain class of functions.