Junyong Zhang

activity

20062022

most citedGeneralized Fibonacci zone plates

32 citations · 233 across the 35 of their papers we have counts for

collaborators

35 papers

math.AP2022

Heat kernel estimate in a conical singular space

Xiaoqi Huang, Junyong Zhang

Let $(X, g)$ be a product cone with the metric $g = d r^{2} + r^{2} h$ , where $X = C (Y) = (0, \infty)_{r} \times Y$ and the cross section $Y$ is a $(n - 1)$ -dimensional closed Riemannian manifold $(Y,h…

math.AP2021

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

Xiaofen Gao, Junyong Zhang, Jiqiang Zheng

We study the dispersive behaviors of two-particles Schrödinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schrödinger and w…

math.AP2021

Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

Luca Fanelli, Junyong Zhang, Jiqiang Zheng

We study the $L^{p} - L^{q}$ -type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an…

math.AP2021

Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications

Yannick Sire, Christopher D. Sogge, Chengbo Wang +1

We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved p…

math.AP2021★ 1 cited

A toy model for the relativistic Vlasov-Maxwell system

Jonathan Ben-Artzi, Stephen Pankavich, Junyong Zhang

The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathemati…

math.AP2021

Global Strichartz estimates for the Dirac equation on symmetric spaces

Jonathan Ben-Artzi, Federico Cacciafesta, Anne-Sophie de Suzzoni +1

In this paper we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension $n \geq 3$ . In particular, we prove estimates for th…

math.AP2021★ 1 cited

Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications

Federico Cacciafesta, Éric Séré, Junyong Zhang

In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an application, we obtain Strichartz e…

math.AP2020★ 1 cited

Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

Junyong Zhang

We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger operators on the flat Euclidean cone $(X, g)$ , where $X=C(\mathbb{S}_σ^1)=(0,\infty)\times \mathbb…

math.AP2020

Generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm magnetic fields

Federico Cacciafesta, Zhiqing Yin, Junyong Zhang

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critica…

math.AP2020★ 1 cited

Strichartz estimates for the Klein-Gordon equation in a conical singular space

Jonathan Ben-Artzi, Federico Cacciafesta, Anne-Sophie de Suzzoni +1

Consider a conical singular space $X = C (Y) = (0, \infty)_{r} \times Y$ with the metric $g = d r^{2} + r^{2} h$ , where the cross section $Y$ is a compact $(n - 1)$ -dimensional closed Riemanni…

math.AP2020

Restriction estimates in a conical singular space: wave equation

Xiaofen Gao, Junyong Zhang, Jiqiang Zheng

We study the restriction estimates in a class of conical singular space $X = C (Y) = (0, \infty)_{r} \times Y$ with the metric $g = d r^{2} + r^{2} h$ , where the cross section $Y$ is a compa…

math.AP2020★ 1 cited

Dispersive estimates for 2D-wave equations with critical potentials

Luca Fanelli, Junyong Zhang, Jiqiang Zheng

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 singulariti…

math.AP2020★ 1 cited

Decay and Strichartz estimates in critical electromagnetic fields

Xiaofen Gao, Zhiqing Yin, Junyong Zhang +1

We study the $L^{1} \to L^{\infty}$ -decay estimates for dispersive equations in the Aharonov-Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation w…

math.AP2019★ 2 cited

Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds

Yannick Sire, Christopher D. Sogge, Chengbo Wang +1

We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates fr…

math.AP2019★ 3 cited

Existence and asymptotics of nonlinear Helmholtz eigenfunctions

Jesse Gell-Redman, Andrew Hassell, Jacob Shapiro +1

We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form \begin{equation*} (Δ- λ^2) u = N[u], \end{equation*} wher…

math.AP2019★ 13 cited

Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

Haruya Mizutani, Junyong Zhang, Jiqiang Zheng

We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let $L_{V} = - Δ + V (x)$ where $Δ$ is the usual Laplacian on $\mathbb{R}^…

math.AP2018★ 12 cited

Nonlinear Schrödinger equation with Coulomb potential

Changxing Miao, Junyong Zhang, Jiqiang Zheng

In this paper, we study the Cauchy problem for the nonlinear Schrödinger equations with Coulomb potential $i \partial_{t} u + Δ u + \frac{K}{∣ x ∣} u = λ ∣ u ∣^{p - 1} u$ with $1 < p \leq 5$ on $\mathbb{R…

math.AP2018★ 18 cited

Strichartz estimates and wave equation in a conic singular space

Junyong Zhang, Jiqiang Zheng

Consider the metric cone $X = C (Y) = (0, \infty)_{r} \times Y$ with the metric $g = d r^{2} + r^{2} h$ where the cross section $Y$ is a compact $(n - 1)$ -dimensional Riemannian manifold $(Y,h…

math.AP2017

Global-in-time Strichartz estimates for Schrodinger on scattering manifolds

Junyong Zhang, Jiqiang Zheng

We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifolds $X^{\circ}$ . Let $L_{V} = Δ_{g} + V$ where $Δ_{g}$ is the Beltrami-…

math.AP2016★ 10 cited

Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space

Junyong Zhang, Jiqiang Zheng

We study the nonlinear Klein-Gordon equation on a product space $M = R \times X$ with metric $g ~ = d t^{2} - g$ where $g$ is the scattering metic on $X$ . We establish the global-in-t…

physics.optics2015★ 2 cited

Three-dimensional array foci of generalized Fibonacci photon sieves

Junyong Zhang, Jie Ke, Jianqiang Zhu +1

We present a new kind of photon sieves on the basis of the generalized Fibonacci sequences. The required numbers and locations of axial foci can be designed by generalized Fibonacc…

math.AP2015★ 11 cited

Scattering theory for the radial $H ˙^{1/2}$ -critical wave Equation with a cubic convolution

Changxing Miao, Junyong Zhang, Jiqiang Zheng

In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution $\partial_{t}^{2} u - Δ u = \pm (∣ x ∣^{- 3} * ∣ u ∣^{2}) u$ in dimensions $d \geq 4$ .…

physics.optics2015★ 32 cited

Generalized Fibonacci zone plates

Jie Ke, Junyong Zhang, Jianqiang Zhu

We propose a family of zone plates which are produced by the generalized Fibonacci sequences and their axial focusing properties are analyzed in detail. Compared with traditional F…

math.AP2015★ 3 cited

Linear adjoint restriction estimates for paraboloid

Changxing Miao, Junyong Zhang, Jiqiang Zheng

We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generali…

Heat kernel estimate in a conical singular space

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications

A toy model for the relativistic Vlasov-Maxwell system

Global Strichartz estimates for the Dirac equation on symmetric spaces

Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications

Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

Generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm magnetic fields

Strichartz estimates for the Klein-Gordon equation in a conical singular space

Restriction estimates in a conical singular space: wave equation

Dispersive estimates for 2D-wave equations with critical potentials

Decay and Strichartz estimates in critical electromagnetic fields

Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds

Existence and asymptotics of nonlinear Helmholtz eigenfunctions

Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

Nonlinear Schrödinger equation with Coulomb potential

Strichartz estimates and wave equation in a conic singular space

Global-in-time Strichartz estimates for Schrodinger on scattering manifolds

Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space

Three-dimensional array foci of generalized Fibonacci photon sieves

Scattering theory for the radial H˙1/2-critical wave Equation with a cubic convolution

Generalized Fibonacci zone plates

Linear adjoint restriction estimates for paraboloid

Scattering theory for the radial $H ˙^{1/2}$ -critical wave Equation with a cubic convolution