Abstract
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.
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This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the RUDN Program of Strategic Academic Leadership.
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Translated by I. Ruzanova
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Korpusov, M.O., Ovsyannikov, E.A. Local Solvability, Blow-up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: I. Green Formulas. Comput. Math. and Math. Phys. 62, 1609–1631 (2022). https://doi.org/10.1134/S096554252209007X
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DOI: https://doi.org/10.1134/S096554252209007X