The initial value problem for a system of modified Korteweg-deVries equations with data that are analytic on $\mathbb{R}$ and having uniform radius of analyticity $r_0$ is studied. After proving an analytic version of known trilinear estimates in Sobolev spaces, local well-posedness is established and persistence of the radius of spatial analyticity is shown till some time $T_0$. Then, for time $t\ge T_0$ it is proved that the radius of spatial analyticity is bounded from below by $c{t}^{-(2+\epsilon )}$, for any $\epsilon >0$.

中文翻译：

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修正的KdV方程组的解析半径的下界

修正Korteweg-deVries方程组的初值问题 $\mathbb{[R}$ 并具有统一的分析半径 ${\mathrm{[R}}_0$被研究。在证明Sobolev空间中已知三线性估计的解析版本后，建立局部适定性并显示空间解析半径的持续时间${Ť}_0$。然后，为了时间$Ť\ge {Ť}_0$ 证明了空间分析的半径是从下面限制的 $C{Ť}^{-（2+\epsilon ）}$，对于任何 $\epsilon >0$。