Scattering for a class of inhomogeneous generalized Hartree equations

Saanouni, Tarek; Peng, Congming

doi:10.1080/00036811.2023.2209100

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Indeed, the global existence versus the blow-up of solutions was obtained. In addition, the scattering under the ground state threshold with spherically symmetric data was proven in [13], and it was extended to the non-radial regime in [14,15]. This paper complements the recent work by Alharbi, G. M. et al [12], in which the authors only considered Equation (1) for b < 0.…”

Section: Introductionsupporting

confidence: 59%

Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations

Almuthaybiri,

Ghanmi,

Saanouni

2023

Mathematics

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The present paper investigates the following inhomogeneous generalized Hartree equation iu˙+Δu=±|u|p−2|x|b(Iα∗|u|p|·|b)u, where the wave function is u:=u(t,x):R×RN→C, with N≥2. In addition, the exponent b>0 gives an unbounded inhomogeneous term |x|b and Iα≈|·|−(N−α) denotes the Riesz-potential for certain 0<α<N. In this work, our aim is to establish the local existence of solutions in some radial Sobolev spaces, as well as the global existence for small data and the decay of energy sub-critical defocusing global solutions. Our results complement the recent work (Sharp threshold of global well-posedness versus finite time blow-up for a class of inhomogeneous Choquard equations, J. Math. Phys. 60 (2019), 081514). The main challenge in this work is to overcome the singularity of the unbounded inhomogeneous term |x|b for certain b>0.

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Section: Introductionsupporting

confidence: 59%

Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations

Almuthaybiri,

Ghanmi,

Saanouni

2023

Mathematics

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Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations

Kim,

Lee,

Seo

2024

Nonlinear Analysis

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Instability of Standing Waves for INLS with Inverse Square Potential

Almuthaybiri,

Saanouni

2024

Mathematics

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This work studies an inhomogeneous generalized Hartree equation with inverse square potential. The purpose is to prove the existence and strong instability of inter-critical standing waves. This means that there are infinitely many data near to the ground state, such that the associated solution blows-up in finite time. The proof combines a variational analysis with the standard variance identity. The challenge is to deal with three difficulties: the singular potential |x|−2, an inhomogeneous term |x|−λ, and a non-local source term.

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Scattering for a class of inhomogeneous generalized Hartree equations

Cited by 3 publications

References 23 publications

Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations

Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations

Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations

Instability of Standing Waves for INLS with Inverse Square Potential

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