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Pure Mathematics 2025

BBM方程在Besov空间 $B_{2, r}^{s} (？)$ 中的全局适定性
Global Well-Posedness for the BBM Equation in Besov Spaces $B_{2, r}^{s} (？)$

DOI: 10.12677/pm.2025.155165, PP. 161-170

陈佳龙

Keywords: Benjamin-Bona-Mahony方程，Besov空间，全局适定性，高低频分解
Benjamin-Bona-Mahony Equation, Besov Spaces, Global Well-Posedness, Low-High Frequency Decomposition

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Abstract:

本文研究了Benjamin-Bona-Mahony (BBM)方程在非齐次Besov空间 $B_{2, r}^{s} (？)$ 中的全局适定性。首先用了压缩映射原理证明了当 $1 \leq p \leq \infty, 1 < r \leq \infty$ 及 $s > \frac{1}{p}$ (或 $1 \leq p \leq \infty$ ， $r = 1$ 及 $s \geq \frac{1}{p}$ )时，BBM方程在 $B_{p, r}^{s} (？)$ 中局部适定的。接着，用高低频分解技巧及算子半群理论证明了当 $1 / 2 < s \leq 1$ ， $2 \leq r < \infty$ 时，BBM方程在 $B_{2, r}^{s} (？)$ 中全局适定。
In this study, we devoted to the global well-posedness for the Benjamin-Bona-Mahony (BBM) equation in the Nonhomogeneous Besov spaces References

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BBM方程在Besov空间 B 2,r s ( ？ )中的全局适定性Global Well-Posedness for the BBM Equation in Besov Spaces B 2,r s ( ？ )

BBM方程在Besov空间 $B_{2, r}^{s} (？)$ 中的全局适定性
Global Well-Posedness for the BBM Equation in Besov Spaces $B_{2, r}^{s} (？)$