On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity
We study the Cauchy problem for the fractional Schrödinger equation iqtu ¼ šm2 Ą DŽa/2u ž
FšuŽ in R1žn, where nb 1, mb 0, 1< a< 2, and F stands for the nonlinearity of Hartree type …
FšuŽ in R1žn, where nb 1, mb 0, 1< a< 2, and F stands for the nonlinearity of Hartree type …
On the orbital stability of fractional Schr\"{o} dinger equations
arXiv:1302.2719v2 [math.AP] 18 Feb 2013 Page 1 arXiv:1302.2719v2 [math.AP] 18 Feb 2013
ON THE ORBITAL STABILITY OF FRACTIONAL SCHRODINGER EQUATIONS YONGGEUN …
ON THE ORBITAL STABILITY OF FRACTIONAL SCHRODINGER EQUATIONS YONGGEUN …
Scattering threshold for the focusing Choquard equation
T Saanouni - Nonlinear Differential Equations and Applications …, 2019 - Springer
Scattering threshold for the focusing Choquard equation | SpringerLink Skip to main content
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Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations
We study the Cauchy problem for the inhomogeneous Hartree equation in this paper.
Although its well-posedness theory has been extensively studied in recent years, much less …
Although its well-posedness theory has been extensively studied in recent years, much less …
On well-posedness for inhomogeneous Hartree equations in the critical case
S Kim - arXiv preprint arXiv:2212.07195, 2022 - arxiv.org
We study the well-posedness for the inhomogeneous Hartree equation $ i\partial_t u+\Delta
u=\lambda (I_\alpha\ast|\cdot|^{-b}| u|^ p)| x|^{-b}| u|^{p-2} u $ in $ H^ s $, $ s\ge0 $. Until …
u=\lambda (I_\alpha\ast|\cdot|^{-b}| u|^ p)| x|^{-b}| u|^{p-2} u $ in $ H^ s $, $ s\ge0 $. Until …
Large data mass-subcritical NLS: critical weighted bounds imply scattering
We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions
with focusing or defocusing nonlinearity. For such equations with critical regularity s_c ∈ …
with focusing or defocusing nonlinearity. For such equations with critical regularity s_c ∈ …
Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity
This paper is devoted to the mathematical analysis of a class of nonlinear fractional
Schrödinger equations with a general Hartree-type integrand. We show the well-posedness …
Schrödinger equations with a general Hartree-type integrand. We show the well-posedness …
Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schrödinger equation with angular regularity
H Hirayama, S Kinoshita, M Okamoto - Journal of Differential Equations, 2024 - Elsevier
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schrödinger
equation in R× R 2 with the nonlinearity η| u| 2 where η∈ C∖{0} and low regularity initial …
equation in R× R 2 with the nonlinearity η| u| 2 where η∈ C∖{0} and low regularity initial …
Global well-posedness for the defocusing 3D quadratic NLS in the sharp critical space
J Shen, Y Wu - arXiv preprint arXiv:2410.04337, 2024 - arxiv.org
In this paper, we prove the global well-posedness of defocusing 3D quadratic nonlinear
Schr\" odinger equation\begin {align*} i\partial_t u+\frac12\Delta u=| u| u,\end {align*} in its …
Schr\" odinger equation\begin {align*} i\partial_t u+\frac12\Delta u=| u| u,\end {align*} in its …
Existence and stability of solitary waves for the inhomogeneous NLS
A Ramadan, AG Stefanov - Physica D: Nonlinear Phenomena, 2020 - Elsevier
In this paper, we identify necessary and sufficient conditions for the existence of
appropriately localized waves for the inhomogeneous semi-linear Schrödinger equation …
appropriately localized waves for the inhomogeneous semi-linear Schrödinger equation …