On the Cauchy problem for Hartree equation in the Wiener algebra

Rémi Carles (1) , Lounes Mouzaoui (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Carles, Lounes Mouzaoui. On the Cauchy problem for Hartree equation in the Wiener algebra. Proceedings of the American Mathematical Society, 2014, 142 (7), pp.2469-2482. ⟨10.1090/S0002-9939-2014-12072-7⟩. ⟨hal-00697812⟩