Abstract
We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity F(u)=(K∗|u|2)u under a specified condition on potential K with Cauchy data in modulation spaces Mp,q(Rd). We establish global well-posedness results in M1,1(Rd) when K(x)=λ|x|−γ(λ∈R,0<γ<min{2,d/2}); in Mp,q(Rd)(1≤q≤min{p,p′} where p′ is the Hölder conjugate of p∈[1,2]) when K is in Fourier algebra FL1(Rd), and local well-posedness result in Mp,1(Rd)(1≤p≤∞) when K∈M1,∞(Rd).
Published Version
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