论文标题
周期性Zakharov-Kuznetsov方程式的Loomis-Whitney-type不平等和较低的规律性良好
Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation
论文作者
论文摘要
在完全周期性的情况下，二维Zakharov-Kuznetsov方程的本地适合性，并证明了Sobolev Spaces $ H^S $，$ S> 1 $的初始数据。频率依赖性时间定位用于控制衍生化非线性。改善先前结果的新成分是非线性织机 - 惠特尼型不平等。
Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in the fully periodic case with initial data in Sobolev spaces $H^s$, $s>1$, is proved. Frequency dependent time localization is utilized to control the derivative nonlinearity. The new ingredient to improve on previous results is a nonlinear Loomis-Whitney-type inequality.
