Global well-posedness for Klein-Gordon-Hartree and fractional Hartree equations on modulation spaces

[摘要] We study the Cauchy problems for the Klein-Gordon (HNLKG), wave (HNLW), and Schrodinger (HNLS) equations with cubic convolution (of Hartree type) nonlinearity. Some global well-posedness and scattering are obtained for the (HNLKG) and (HNLS) with small Cauchy data in some modulation spaces. Global well-posedness for fractional Schrodinger (fNLSH) equation with Hartree type nonlinearity is obtained with Cauchy data in some modulation spaces. Local well-posedness for (HNLW), (fHNLS) and (HNLKG) with rough data in modulation spaces is shown. As a consequence, we get local and global well-posedness and scattering in larger than usual -Sobolev spaces.

[学科分类] 数学（综合）

[关键词] Klein-Gordon-Hartree equation;fractional Hartree equation;wave-Hartree equation;well-posedness;modulation spaces;small initial data.