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arXiv · 2212.08575

Global strong solutions of the coupled Klein-Gordon-Schr\"{o}dinger equations

Tohru Ozawa·Kenta Tomioka
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Abstract

We study the initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$. The method of the construction of global strong solutions depends on the proof that solutions of regularized systems by the Yosida approximation form a bounded sequence in $H^2 \oplus H^2 \oplus H^1$ and a convergent sequence in $H^1 \oplus H^1 \oplus L^2$. The method of proof is independent of the Brezis-Gallouet technique and a compactness argument.

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Tohru Ozawa, Kenta Tomioka. 2022-12-16. Global strong solutions of the coupled Klein-Gordon-Schr\"{o}dinger equations. https://arxiv.org/abs/2212.08575

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