On the global existence of semirelativistic Hartree equations

Abstract

In this paper we brief some recent results on the global well-posedness of semirelativistic Hartree type equations. Then we improve the theories for radial solutions developed in [6] and extend them to nonradial cases. 1 Problems and results We consider the following Cauchy problem: { i∂tu = √ 1−∆ u+ F (u) in R × R, n ≥ 1, u(x, 0) = φ(x) in R. (1.1) Here F… (More)

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