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[کتاب][B] Introduction to nonlinear dispersive equations
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 …
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
We consider the focusing cubic nonlinear Schrödinger equation with inverse-square
potential in three space dimensions. We identify a sharp threshold between scattering and …
potential in three space dimensions. We identify a sharp threshold between scattering and …
The energy-critical NLS with inverse-square potential
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 …
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
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 …
critical rough potential of a| x|− 2 type. The new ingredients are the interaction Morawetz …
Dispersive estimates for 2D-wave equations with critical potentials
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 …
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
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 …
the Schrödinger operator with inverse-square potential\begin {equation*}\mathcal L_a …
Decay and Strichartz estimates in critical electromagnetic fields
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 …
Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation …
Time decay of scaling invariant electromagnetic Schrödinger equations on the plane
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 …
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
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 …
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
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 …
equation perturbed by an Aharonov--Bohm magnetic field. Our main results will be a family …