[کتاب][B] Introduction to nonlinear dispersive equations

F Linares, G Ponce - 2014‏ - books.google.com
This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …

The focusing cubic NLS with inverse-square potential in three space dimensions

R Killip, J Murphy, M Visan, J Zheng - 2017‏ - projecteuclid.org
We consider the focusing cubic nonlinear Schrödinger equation with inverse-square
potential in three space dimensions. We identify a sharp threshold between scattering and …

The energy-critical NLS with inverse-square potential

R Killip, C Miao, M Visan, J Zhang, J Zheng - arxiv preprint arxiv …, 2015‏ - arxiv.org
We consider the defocusing energy-critical nonlinear Schr\" odinger equation with inverse-
square potential $ iu_t=-\Delta u+ a| x|^{-2} u+| u|^ 4u $ in three space dimensions. We …

[HTML][HTML] Scattering theory for nonlinear Schrödinger equations with inverse-square potential

J Zhang, J Zheng - Journal of Functional Analysis, 2014‏ - Elsevier
We study the long-time behavior of solutions to nonlinear Schrödinger equations with some
critical rough potential of a| x|− 2 type. The new ingredients are the interaction Morawetz …

Dispersive estimates for 2D-wave equations with critical potentials

L Fanelli, J Zhang, J Zheng - Advances in Mathematics, 2022‏ - Elsevier
We study the 2D-wave equation with a scaling-critical electromagnetic potential. This
problem is doubly critical, because of the scaling invariance of the model and the …

The 𝑊^{𝑠, 𝑝}-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

C Miao, X Su, J Zheng - Transactions of the American Mathematical Society, 2023‏ - ams.org
In this paper, we investigate the $ W^{s, p} $-boundedness for stationary wave operators of
the Schrödinger operator with inverse-square potential\begin {equation*}\mathcal L_a …

Decay and Strichartz estimates in critical electromagnetic fields

X Gao, Z Yin, J Zhang, J Zheng - Journal of Functional Analysis, 2022‏ - Elsevier
We study the L 1→ L∞-decay estimates for the Klein-Gordon equation in the Aharonov-
Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation …

Time decay of scaling invariant electromagnetic Schrödinger equations on the plane

L Fanelli, V Felli, MA Fontelos, A Primo - Communications in Mathematical …, 2015‏ - Springer
Time Decay of Scaling Invariant Electromagnetic Schrödinger Equations on the Plane Page 1
Digital Object Identifier (DOI) 10.1007/s00220-015-2291-2 Commun. Math. Phys. 337 …

[HTML][HTML] Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential

H Mizutani - Journal of Differential Equations, 2017‏ - Elsevier
The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the
Schrödinger equation on R n, n≥ 3, with the negative inverse-square potential− σ| x|− 2 in …

Dispersive estimates for Dirac equations in Aharonov-Bohm magnetic fields: massless case

F Cacciafesta, P D'Ancona, Z Yin, J Zhang - arxiv preprint arxiv …, 2024‏ - arxiv.org
In this paper we study the dispersive properties of a two dimensional massless Dirac
equation perturbed by an Aharonov--Bohm magnetic field. Our main results will be a family …