论文标题
耦合的klein-gordon-schrödinger方程的全球强解决方案
Global strong solutions of the coupled Klein-Gordon-Schrödinger equations
论文作者
论文摘要
我们研究了$ \ Mathbb r^n $的耦合klein-gordon-schrödinger方程的初始价值问题，带有$ n \ leq 4 $。在初始数据的自然假设下，我们证明了$ h^2 \ oplus h^2 \ oplus h^1 $中全局解决方案的存在和独特性。构建全球强溶液的方法取决于证据，即通过Yosida近似的正规化系统的解决方案形成了$ h^2 \ oplus h^2 \ oplus h^1 $中的一个有界序列，而在$ h^1 \ oplus h^1 \ oplus h^1 \ oplus lus l^2 $中的收敛序列。证明方法独立于布雷兹 - 加卢埃特技术和紧凑的论点。
We study the initial-boundary value problem for the coupled Klein-Gordon-Schrödinger 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.
