关于Kadomtsev-Petviashvilli（KPII）方程解的正则性传播
On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation
摘要：
我们将推导出与KPII方程相关的IVP解的一些特殊的正则性。主要地，对于数据$u_0\in X_s(\mathbb R^2)$，$s>2$，（见下面的（1.2）），对于某些$m\in\mathbb Z^+,\,m\geq 3,$和$x_0\in \mathbb R$，其限制属于$H^m((x_0,\infty)\times\mathbb R)$，我们将证明对于任何$β\in \mathbb R$和任何$t>0$，相应解$u(\cdot,t)$的限制属于$H^m((β,\infty)\times\mathbb R)$。
英文摘要：
We shall deduce some special regularity properties of solutions to the IVP associated to the KPII equation. Mainly, for datum $u_0\in X_s(\mathbb R^2)$, $s>2$, (see (1.2) below) whose restriction belongs to $H^m((x_0,\infty)\times\mathbb R)$ for some $m\in\mathbb Z^+,\,m\geq 3,$ and $x_0\in \mathbb R$, we shall prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^m((β,\infty)\times\mathbb R)$ for any $β\in \mathbb R$ and any $t>0$.
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