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Print ISSN : 0532-8721
Small Data Scattering of Hartree Type Fractional Schrödinger Equations in a Scaling Critical Space
Yonggeun ChoTohru OzawaChanghun Yang
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2021 Volume 64 Issue 1 Pages 1-15

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Abstract

In this paper we study the small-data scattering of Hartree type fractional Schrödinger equations in space dimension 2, 3. It has Lévy index α between 1 and 2, and Hartree type nonlinearity F(u) = μ(|x| * |u|2)u with 2d/(2d-1) < γ < 2, γ ≥ α > 1. This equation is scaling-critical in sc with sc = (γ-α)/2. We show that the solution scatters in sc,1, where sc,1 is also a scaling critical space of Sobolev type taking in angular regularity with norm defined by ||ϕ||sc,1 = ||ϕ||sc + ||∇Sϕ||sc. For this purpose we use the recently developed Strichartz estimate which is Lθ2-averaged on the unit sphere Sd-1.

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© 2021 by the Division of Functional Equations, The Mathematical Society of Japan
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