论文标题
KP-I方程的规律性低适合性：分散式案例
Low regularity well-posedness for KP-I equations: the dispersion-generalized case
论文作者
论文摘要
我们在$ \ mathbb {r}^2 $中证明了分散式kadomtsev-petviashvili i方程的新良好结果，该方程将经典的kp-i方程与第五阶KP-i方程联系起来。对于足够强大的分散，我们在$ l^2（\ mathbb {r}^2）$中显示了全球适应性。为此，我们将共鸣和横向注意事项与Strichartz估计值和非线性织布（Whitney Normis）结合在一起。此外，我们证明，对于小分散，无法通过PICARD迭代来解决方程。在这种情况下，我们使用额外的频率依赖时间定位。
We prove new well-posedness results for dispersion-generalized Kadomtsev--Petviashvili I equations in $\mathbb{R}^2$, which family links the classical KP-I equation with the fifth order KP-I equation. For strong enough dispersion, we show global well-posedness in $L^2(\mathbb{R}^2)$. To this end, we combine resonance and transversality considerations with Strichartz estimates and a nonlinear Loomis--Whitney inequality. Moreover, we prove that for small dispersion, the equations cannot be solved via Picard iteration. In this case, we use an additional frequency dependent time localization.
