AI 中文总结
研究Fokas - Olver - Rosenau - Qiao方程在临界Sobolev空间的情况，通过构造满足爆破准则的显式初始数据，证明其在\(H^{5/2}(\mathbb{R})\)中的范数膨胀，补充了该方程的适定性理论。
AI 中文摘要
本文证明了Fokas - Olver - Rosenau - Qiao方程（一种具有三次非线性的修正Camassa - Holm型方程）在临界Sobolev空间\(H^{5/2}(\mathbb{R})\)中的范数膨胀。该结果补充了此方程的适定性理论，此前已知该方程在\(s>5/2\)时在\(H^{s}(\mathbb{R})\)中局部适定。证明依赖于构造满足Fokas - Olver - Rosenau - Qiao方程先前已知爆破准则的显式初始数据。
英文摘要
This article proves norm inflation in the critical Sobolev space $H^{5/2}(\mathbb{R})$ for the Fokas-Olver-Rosenau-Qiao equation, which is a modified Camassa-Holm-type equation with cubic nonlinearity. This result complements the well-posedness theory for this equation, which was previously known to be locally well-posed in $H^{s}(\mathbb{R})$ for $s>5/2$. The proof relies on the construction of explicit initial data satisfying the previously known blow-up criteria for the Fokas-Olver-Rosenau-Qiao equation, a step that appears to be of independent interest.
