Trilinear L estimates with applications to the Cauchy problem for the Hartree-type equation
Trilinear L estimates with applications to the Cauchy problem for the Hartree-type equation
复制标题
三线性 L 估计及其对 Hartree 型方程柯西问题的应用
DOI：
10.1016/j.jmaa.2018.09.014
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发表时间：
2019
影响因子：
1.3
通讯作者：
Hyakuna Ryosuke
中科院分区：
文献类型：
--
作者：
Hoshino Gaku;Hyakuna Ryosuke
本文证明了一类具有Hartree型非线性项的三线性算子的Lp估计.作为这些估计的应用，证明了在对初值作一定的正则性假设下，Hartree型方程的Cauchy问题在线性变换后在Bessel势和齐次Besov空间中成为局部适定的.适定性的概念和求解方程的函数框架是由Y。舟
In this paper, L p estimates for a trilinear operator associated with the Hartree type nonlinearity are proved. Moreover, as application of these estimates, it is proved that after a linear transformation, the Cauchy problem for the Hartree-type equation becomes locally well posed in the Bessel potential and homogeneous Besov spaces under certain regularity assumptions on the initial data. This notion of well-posedness and the functional framework to solve the equation were firstly proposed by Y. Zhou.