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- W4367335700 abstract "We study the well-posedness for the inhomogeneous Hartree equation $ ipartial_t u + Delta u = lambda(I_alpha ast |cdot|^{-b}|u|^p)|x|^{-b}|u|^{p-2}u $ in $ H^s $, $ sge0 $. Until recently, its well-posedness theory has been intensively studied, focusing on solving the problem for the critical index $ p = 1+frac{2-2b+alpha}{n-2s} $ with $ 0le s le 1 $, but the case $ 1/2leq s leq 1 $ is still an open problem. In this paper, we develop the well-posedness theory in this case, especially including the energy-critical case. To this end, we approach to the matter based on the Sobolev-Lorentz space which can lead us to perform a finer analysis for this equation. This is because it makes it possible to control the nonlinearity involving the singularity $ |x|^{-b} $ as well as the Riesz potential $ I_alpha $ more effectively." @default.
- W4367335700 created "2023-04-30" @default.
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- W4367335700 date "2023-01-01" @default.
- W4367335700 modified "2023-09-26" @default.
- W4367335700 title "On well-posedness for inhomogeneous Hartree equations in the critical case" @default.
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- W4367335700 doi "https://doi.org/10.3934/cpaa.2023060" @default.
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