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. [ABSTRACT FROM AUTHOR]