On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation

Abstract

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 $m\in {\mathbb{Z}}^{+},m\ge 3,$ and $x_0\in \mathbb{R}$, we shall prove that the restriction of the corresponding solution $u(\cdot ,t)$ belongs to $H^m((\beta ,\infty )\times \mathbb{R})$ for any $\beta \in \mathbb{R}$ and any $t>0$.

Cited by in corpus (1)

• On the regularity of solutions to a class of nonlinear dispersive equations