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The mixed fractional Hartree equations in Fourier amalgam and modulation spaces (2302.10683v1)

Published 21 Feb 2023 in math.AP

Abstract: We prove local and global well-posedness for mixed fractional Hartree equation with low regularity Cauchy data in Fourier amalgam $\widehat{w}{p,q}$ and modulation $M{p,q}$ spaces. Similar results also hold for the Hartree equation with harmonic potential in some modulation spaces. Our approach also addresses Hartree-Fock equations of finitely many particles. A key ingredient of our method is to establish trilinear estimates for Hartree non-linearity and the use of Strichartz estimates. As a consequence, we could gain $\widehat{w}{p,q}$ and $M{p,q}-$regularity for all $p,q\in [1, \infty].$ Thus we could solve new problems, extends and complements several previous results (including Sobolev $Hs-$regularity results).

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