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

Electronic Journal of Differential Equations

article

Divyang G. Bhimani¹ 

[1] Department of Mathematics Indian Institute of Science Education and Research Dr. Homi Bhabha Road

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

DOI  :  10.58997/ejde.2021.101

学科分类：数学（综合）

来源: Texas State University

【 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.

【 授权许可】

CC BY