论文标题
在傅立叶 - lebesgue空间中修改的KDV方程的精致良好的结果
A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces
论文作者
论文摘要
我们以低规律性在圆圈上研究了复杂值修改的Korteweg-de Vries方程（MKDV）的适当性。在我们以前的工作（2019年）中，我们根据动量的保护引入了第二个重归于MKDV方程，我们建议将其作为正确的模型，用于研究$ H^\ frac12（\ Mathbb {t}）$ H^\ frac12（\ Mathbb {t}）$的复杂值MKDV。在这里，我们采用了Deng-Nahmod-Yue（2019）介绍的方法来证明在傅立叶 - lebesgue Spaces $ \ Mathcal {f} l^{s，p}（\ Mathbb {t}）$ $ s \ geq frac \ frac \ frac $ p <fe \ p <和$ p <和$ p <p <和$ p <p <和$ p <p <和$ p <作为这种良好的结果的副产品，我们显示了复杂值的MKDV的不良性，而在这些傅立叶 - 文密空间中，具有无限动量的初始数据的第二次重新归一化。
We study the well-posedness of the complex-valued modified Korteweg-de Vries equation (mKdV) on the circle at low regularity. In our previous work (2019), we introduced the second renormalized mKdV equation, based on the conservation of momentum, which we proposed as the correct model to study the complex-valued mKdV outside of $H^\frac12(\mathbb{T})$. Here, we employ the method introduced by Deng-Nahmod-Yue (2019) to prove local well-posedness of the second renormalized mKdV equation in the Fourier-Lebesgue spaces $\mathcal{F}L^{s,p}(\mathbb{T})$ for $s\geq \frac12$ and $1\leq p <\infty$. As a byproduct of this well-posedness result, we show ill-posedness of the complex-valued mKdV without the second renormalization for initial data in these Fourier-Lebesgue spaces with infinite momentum.
