论文标题
在关键的BESOV空间中，全球及时的可溶性和爆炸性和爆炸
Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space
论文作者
论文摘要
在本文中，我们证明了在关键的BESOV空间中非同一两组式CAMASSA-HOLM系统的强大解决方案的全球HADAMARD适用性$ b_ {2,1}^{\ frac {1} {1} {2} {2}}}}}（\ Mathbb {t}）$。我们的结果表明，与经典Camassa-Holm型方程式的著名作品相比，全球解决方案的存在仅依赖于可变系数$α（t）$和$γ（t）$的$ l^1 $ - 积分性，但与初始数据的形状或光滑度无关。证明的关键要素取决于对两种组件形式之间相互效应的仔细分析，即近似溶液的统一结合以及通过Littlewood-Paley-Paley分解理论对低规度BESOV空间中立方非线性的几种关键估计。我们结果中的案例减少的情况下，在贝斯维托空间中为两种具有弱耗散术语的众所周知的众所周知的峰峰系统的全球解决方案存在。 $α（t）$ an $γ（t）$。
In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space $B_{2,1}^{\frac{1}{2}}(\mathbb{T})$. Our results shows that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the $L^1$-integrability of the variable coefficients $α(t)$ and $γ(t)$, but nothing to do with the shape or smoothness of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in low-regularity Besov spaces via the Littlewood-Paley decomposition theory. A reduced case in our results yields the global existence of solutions in a Besov space for two kinds of well-known isospectral peakon system with weakly dissipative terms.} Moreover, we derive two kinds of precise blow-up criteria for a strong solution in both critical and non-critical Besov spaces, as well as providing specific characterization for the lower bound of the blow-up time, which implies the global existence with additional conditions on the time-dependent parameters $α(t)$ an $γ(t)$.
