Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415021 | Journal of Functional Analysis | 2016 | 27 Pages |
Abstract
We consider the Cauchy problem for the Hartree equation in space dimension dâ¥3. We assume that the interaction potential V belongs to the weak Ld/2 space. We prove that if the initial data Ï is sufficiently small in the L2-sense and either Ï or its Fourier transform FÏ satisfies a real-analytic condition, then the solution u(t) is also real-analytic for any tâ 0. We also prove that if Ï and V satisfy some strong condition, then u(t) can be extended to an entire function on Cd for any tâ 0. A part of our method is applicable to the final value problem. We remark that no L2 smallness condition is imposed on first and higher order partial derivatives of Ï and FÏ.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hironobu Sasaki,