On the Propagation of Regularity of Solutions of the Kadomtsev--Petviashvili Equation
| Autor: | Gustavo Ponce, Felipe Linares, Pedro Isaza |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | SIAM Journal on Mathematical Analysis. 48:1006-1024 |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/15m1012098 |
| Popis: | We shall deduce some special regularity properties of solutions to the IVP associated to the Kadomtsev--Petviashvili 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 $H^m((\beta,\infty)\times\mathbb{R})$ for any $\beta\in \mathbb{R}$ and any $t>0$. |
| Databáze: | OpenAIRE |
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