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- W2898243281 abstract "We study Cauchy problem for the Klein-Gordon (HNLKG), wave (HNLW) and Schrodinger (HNLS) equations with cubic convolution (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. This improves known results in Sobolev spaces in some sense. As a consequence, we get local and global well-posedness and scattering in larger than usual $L^p-$Sobolev spaces and we could include wider class of Hartree type nonlinarity." @default.
- W2898243281 created "2018-11-02" @default.
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- W2898243281 date "2018-10-26" @default.
- W2898243281 modified "2023-09-27" @default.
- W2898243281 title "Global Cauchy problems for the Klein-Gordon, wave and fractional Schrödinger equations with Hartree nonlinearity on modulation spaces" @default.
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