Bhimani, Divyang2022-11-042022-11-042021-12-21Bhimani, D. G. (2021). Global well-posedness for Klein-Gordon-Hartree and fractional Hartree equations on modulation spaces. <i>Electronic Journal of Differential Equations, 2021</i>(101), pp. 1-23.1072-6691https://hdl.handle.net/10877/16283We 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 Lp -Sobolev spaces.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalKlein-Gordon-Hartree equationFractional Hartree equationWave-Hartree equationWell-posednessModulation spacesSmall initial dataArticle