## On the Cauchy problem for the Hartree type equation in the Wiener algebra

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- by Rémi Carles and Lounès Mouzaoui
- Proc. Amer. Math. Soc.
**142**(2014), 2469-2482 - DOI: https://doi.org/10.1090/S0002-9939-2014-12072-7
- Published electronically: March 17, 2014
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## Abstract:

We consider the mass-subcritical Hartree equation with a homogeneous kernel in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally well-posed if we simply work in the space of functions whose Fourier transform is integrable. Similar results are proven when the kernel is not homogeneous and is such that its Fourier transform belongs to some Lebesgue space.## References

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## Bibliographic Information

**Rémi Carles**- Affiliation: Mathématiques, CC 051, CNRS and Université Montpellier 2, 34095 Montpellier, France
- ORCID: 0000-0002-8866-587X
- Email: Remi.Carles@math.cnrs.fr
**Lounès Mouzaoui**- Affiliation: Mathématiques, CC 051, CNRS and Université Montpellier 2, 34095 Montpellier, France
- Email: lounes.mouzaoui@univ-montp2.fr
- Received by editor(s): May 16, 2012
- Received by editor(s) in revised form: July 17, 2012, and August 1, 2012
- Published electronically: March 17, 2014
- Additional Notes: This work was supported by the French ANR project R.A.S. (ANR-08-JCJC-0124-01)
- Communicated by: James E. Colliander
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**142**(2014), 2469-2482 - MSC (2010): Primary 35Q55; Secondary 35A01, 35B30, 35B45, 35B65
- DOI: https://doi.org/10.1090/S0002-9939-2014-12072-7
- MathSciNet review: 3195768