Global well-posedness for Klein-Gordon-Hartree and fractional Hartree equations on modulation spaces
Date
2021-12-21
Authors
Bhimani, Divyang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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 Lp -Sobolev spaces.
Description
Keywords
Klein-Gordon-Hartree equation, Fractional Hartree equation, Wave-Hartree equation, Well-posedness, Modulation spaces, Small initial data
Citation
Bhimani, 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.
Rights
Attribution 4.0 International