作者：苗长兴¹;，张军勇^2,3;，郑继强¹; （¹Institute of Applied Physics and Computational Mathematics；²Department of Mathematics,Beijing Institute of Technology；³Department of Mathematics,Cardiff University）

出处：Acta Mathematica Scientia(English Series) 2022

关键词：nonlinear；Schrödinger；equations；long；range；potential；global；well-posedness；blow-up；scattering

摘要：In this paper,we study the Cauchy problem for the nonlinear Schr?dinger equations with Coulomb potential i?_tu+Δu+K/|x|u=-λ|u|^p-1 ...

作者：Changxing MIAO，Junyong ZHANG，Jiqiang ZHENG （Institute of Applied Physics and Computational Mathematics，Beijing 100088，China；Department of Mathematics，Beijing Institute of Technology，Beijing 100081，China；Department of Mathematics，Cardiff University，UK）

出处：数学物理学报(英文版) 2022

关键词：nonlinear；Schr?dinger；equations；long；range；potential；global；well-posedness；blow-up；scattering

摘要：In this paper,we study the Cauchy problem for the nonlinear Schr?dinger equa-tions with Coulomb potential i?tu+Δu+K/|x|u=λ|u|p-1u with 1＜p≤5 on R3.Our ...

作者：Fanelli, Luca;Zhang, Junyong;Zheng, Jiqiang （¹Ikerbasque, Universidad del País Vasco, Departamento de Matemáticas, Bilbao, Spain;²Department of Mathematics, Beijing Key Laboratory on Mathematical Characterization, Analysis, and Applications of Complex Information, Beijing Institute of Technology, Beijing, 100081, China;³Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China）

出处：Advances in Mathematics 2022

摘要：We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of ...

作者：Ben-Artzi, Jonathan;Cacciafesta, Federico;de Suzzoni, Anne Sophie;Zhang, Junyong （¹School of Mathematics, Cardiff University, Senghennydd Road, Wales, Cardiff, CF24 4AG, United Kingdom;²Dipartimento di Matematica, Universitá Degli Studi di Padova, Via Trieste, 63, Padova, 35131, Italy;³Cmls, École Polytechnique, Cnrs, Université Paris- Saclay, PALAISEAU Cedex, 91128, France;⁴Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China）

出处：Forum of Mathematics, Sigma 2022

摘要：In this paper, we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension. In particular, we ...

作者：Huang, Xiaoqi;Zhang, Junyong （¹Department of Mathematics, University of Maryland, College Park; MD; 20742, United States;²Department of Mathematics, Beijing Institute of Technology, Beijing; 100081, China）

出处：arXiv 2022

摘要：Let (X, g) be a product cone with the metric g = dr2+ r2h, where X = C(Y) = (0, ∞)r×Y and the cross section Y is a (n-1)-dimensional closed Riemannian ...

作者：Xiaofen Gao;Junyong Zhang;Jiqiang Zheng （¹Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, China;²Department of Mathematics, Beijing Key Laboratory on Mathematical Characterization, Analysis, and Applications of Complex Information, Beijing Institute of Technology, 100081, Beijing, China;³Institute of Applied Physics and Computational Mathematics, 100088, Beijing, China）

出处：Journal of Fourier Analysis and Applications 2022

关键词：Adjoint restriction estimates;Keel–Smith–Sogge estimate;Conical singular space;Inverse-square potential;Wave equation

摘要：We study the restriction estimates in a class of conical singular space X=C(Y)=(0, infty )_r times Y with the metric g= mathrm {d}r^2+r^2h, where the ...

作者：Miao, Changxing¹;Zhang, Junyong^2,3;Zheng, Jiqiang¹; （¹Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China;²Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China;³Department of Mathematics, Cardiff University, Cardiff, United Kingdom）

出处：Acta Mathematica Scientia 2022

关键词：GLOBAL WELL-POSEDNESS;CAUCHY-PROBLEM;POSITIVE SOLUTIONS;SCATTERING-THEORY;THOMAS-FERMI;GROUND-STATE;TIME DECAY;EXISTENCE;OPERATORS;UNIQUENESS

摘要：In this paper, we study the Cauchy problem for the nonlinear Schrödinger equations with Coulomb potential $${\rm{i}}{\partial _t}u + \Delta u + {K \ov ...

作者：Miao, Changxing¹;Zhang, Junyong^2,3,4;Zheng, Jiqiang²; （¹Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P.O. Box 8009, China;²The Graduate School of China Academy of Engineering Physics, Beijing, 100088, P.O. Box 2101, China;³Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China;⁴Beijing Computational Science Research, Beijing 100084, China）

出处：Proc. Amer. Math. Soc. 2012

摘要：This paper is devoted to the study of the restriction problem in harmonic analysis. Based on the spherical harmonics expansion and analyzing the asymp ...

作者：Luca Fanelli;Junyong Zhang;Jiqiang Zheng （¹Ikerbasque and Universidad del País Vasco , Departamento de Matemáticas, Bilbao, Spain;²Department of Mathematics , Beijing Institute of Technology, Beijing 100081;³Institute of Applied Physics and Computational Mathematics , Beijing 100088）

出处：International Mathematics Research Notices

摘要：We study the |$L^{p}-L^{q}$|-type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov ...

作者：Federico Cacciafesta;Éric Séré;Junyong Zhang （¹a Dipartimento di Matematica, Universitá degli studi di Padova, Padova, Italy;²b CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, PSL Research University, Paris Cedex 16, France;³c Department of Mathematics, Beijing Institute of Technology, Beijing, China）

出处：Communications in Partial Differential Equations

关键词：Dirac-Coulomb equation;Strichartz estimates;steepest discent method

摘要：In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an appli ...