Publications of S. Zheng

Thus we might eventually find harmony in chaos...

• S. Zheng, Spectral Multipliers for Magnetic Schrödinger Operatorsa. La Matematica (2024).  
• O. Asipchuk, C. Leonard, S. Zheng, Existence and non-existence of ground state solutions for magnetic NLS. arXiv (2024)  
• M. Beceanu, T.J. Luo, and S.Zheng, Existence and stability for Fourth order NLS with a decaying potential. Preprint.
• Yi H., Y. Lee, S. Zheng, (2024). Damped Nonlinear Schrödinger Equation with Stark Effect. Nonlinear and Modern Mathematical Physics 2022. Springer Proceedings in Mathematics & Statistics, Vol 459, pp 189-205 (book chapter)
• Sobolev and Besov embeddings for Schrödinger operators. 
• Profile decomposition for fractional quantum oscillators.
• Y. Hu, Yongki Lee and S. Zheng, Shock formation in traffic flow models with nonlocal look ahead and behind flux. arXiv (2023), book chapter to appear in "Applied Mathematical Analysis and Computation", 1st SGMC, Proceedings of Mathematics & Statistics, Springer
  
• C. Leonard and S. Zheng, Note on rotating BEC under a confining potential. Partial Differential Equations in Applied Mathematics, 2022, Elsevier
• (with Nyla B., Hichem H. and Yi H.) Threshold for blowup and stability for NLS with rotation. Annales Henri Poincaré   Vol.24, p.1377–1416, (2023)
  
• (with Y. Hu and C. Leonard), Universal upper bound on the blowup rate of nonlinear Schrödinger equation with rotation. In Excursions in Harmonic Analysis, Volume 6. In Honor of John Benedetto's 80th Birthday, edited by M. Hirn, S. Li, K. Okoudjou, S. Saliani, O. Yilmaz, Book series Applied and Numerical Harmonic Analysis. 2021. Springer Nature, Switzerland.
• (with Ting-Jian Luo and Shi-Hui Zhu) The Existence and Stability of Normalized Solutions for a Bi-Harmonic Nonlinear Schrödinger Equation with Mixed Dispersion.  Acta Mathematica Scientia,  doi  (2023).
• (with Nyla Basharat and Yi Hu) Blowup rate for mass critical rotational nonlinear Schrödinger equations. Contemporary Math. 725, 2019. arXiv
• (with Jian Zhang and Shihui Zhu) Orbital stability of standing waves for fractional Hartree equation with unbounded potentials, to appear
• Nonlinear dispersive waves and fluids.
      Editors: Marius Beceanu, Jerry Bona, Geng Chen, Tuoc Van Phan, Avy Soffer and Shijun Zheng.
      Contemporary Mathematics, Volume 725, AMS Book Series 2019.
  
• Partial Differential Equations and Function Spaces. Special Issue.
  Editors: Shijun Zheng, Simone Secchi, Huoxiong Wu, and Nguyen C. Phuc, Journal of Function Spaces 2016 Hindawi Publishing.
• (with L. Galati) Nonlinear Schrödinger equations for Bose-Einstein condensates. Nonlinear and Modern Mathematical Physics 2013
• Fractional regularity for  nonlinear Schrödinger equations with magnetic fields. Contemp. Math. 581 (2012) pp.271–285.
•      Recent Advances in Harmonic Analysis and Partial Differential Equations.
          Editors: Andrea Nahmod, Christopher Sogge, Xiaoyi Zhang and Shijun Zheng.
            Contemporary Mathematics, Volume 581, AMS Book Series 2012.
  

• Spectral multipliers for Schrödinger operators, Illinois Journal of Mathematics, Volume 54, No.2.  2010/2011.
  
• Note on gradient estimates of heat kernel for Schrödinger operators, Applied Mathematics 2010.
• (with Z. Zhang) Strichartz estimates and local wellposedness for the Schrödinger equation with the twisted sub-Laplacian, Proceedings of the Centre for Mathematics and its Applications. The Australian National University, Canberra 2010.
  
• (with J.J. Benedetto) Besov spaces for the Schrödinger operator with barrier potential, Complex Analysis and Operator Theory, 2010, Birkhäuser.
• Interpolation theorems for self-adjoint operators, Anal. Theory Appl. Volume 25, No. 1, 2009, 79-85.
• (with G. Olafsson) Harmonic analysis related to Schrödinger operators, Contemporary Mathematics. AMS Volume 464 (2008), 213-230.
• Time decay for Schrödinger equation with rough potentials, Anal. Theory Appl. Vol.23(4), 2007.  
• Spectral calculus for Schrödinger operators in one and three dimensions, Preprint
• Time decay of quantum waves on Riemannian manifolds, Presented at AMS Conferences 2007.
• On the semilinear wave equation on Riemannian symmetric spaces, Preprint.
• Littlewood-Paley theorem for Schrödinger operators, Anal. Theory Appl. 22(4), 2006. Springer Verlag.
• (with G. Olafsson) Function spaces associated with Schrödinger operators: the Pöschl-Teller potential,
       Journal of Fourier Analysis and Applications 12(6), 2006  also in Archiv
• A representation formula related to Schroedinger operators,  Anal. Theory Appl. 20(3), (2004) also in Archiv  Zentralblatt Math
• Dispersive estimates for wave and Schrödinger equations with potentials near L^n/2(Rⁿ) (In preparation).
• (with G. Olafsson, K. Oskolkov) Spectral multipliers for Schrödinger operators, II.
• Schrödinger equation with magnetic potential of polynomial growth: Eigenfunction concentration.
  
• Lecture on Schrödinger operators:  Harmonic analysis and PDE   (in preparation).   Topics in Geometric analysis and Mathematical Physics
  
• Dissertation, Besov spaces for Schrödinger operators, University of Maryland, College Park, 2003.

• Weak type estimates of Bochner-Riesz means on Riemannian symmetric spaces. Preprint.
• S. Zheng, Perturbed Fourier transform for Schrödinger operators. Springer Proceedings in Mathematics & Statistics, Applied Mathematical Analysis and Computations, Volume I. Oct. 2024.
• (with G. Olafsson) Wavelets, Besov spaces and integral representations.
• Multipliers of Hardy spaces on  p-adic number fields
• Cesaro summability of Hardy space on the ring of integers in a local field,   J. Math. Anal. Appl., 249, (2000). Zentralblatt Math
• Riesz type kernels over the ring of integers of a local field,   J. Math. Anal. Appl., 208, (1997).  Zentralblatt Math
• (with Weiyi Su), L^p estimates for the iterated Hardy-Littlewood maximal operator, Approx. Theory Appl., 14 (3), (1998).   Zentralblatt Math
• L^p estimates for the iterated Hardy-Littlewood maximal operator, II
• (with Weixing Zheng), Almost everywhere convergence of sequences of multiplier operators on local fields, Science in China, 40 (1), (1997)   Springer-Verlag. Zentralblatt Math
• (with Weixing Zheng) Remarks on self-similar fractal sets. Journal of Nanjing University (Mathematics) 16 (1999), no.1, 1-7.    Zentralblatt Math
  
• (with Jianming Liu) A note on Riesz means over the ring of p-adic integers. Journal of Nanjing University (Mathematics) . 13 (1996), no. 1, 58-63.  Zentralblatt Math
• Translation from the English version Encyclopedia of Mathematics, Natural Science Press, Beijing, 1995.
• On Riesz type kernels over local fields. Approx. Theory Appl. 11 (1995), no. 4, 24--34.  Zentralblatt Math
• Representation theorems on local fields. Journal of Nanjing University. (Natural Sci. Ed.) 29 (1993), no. 4, 533--540.  Zentralblatt Math

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  Computational harmonic analysis and numerical modeling

• J. Cornthwaite, C. Zhang and S. Zheng, "Pressure-Poisson method for 2D incompressible Navier-Stokes equations using FEM”. Preliminary Report.
• Multiscale reconstruction and nonlinear diffusion problem in image processing.
• (with J.J. Benedetto, D.M. Healy and I. Konstantinidis) Report on recent progress on the TAIP project (Thin Film Analog Image Processing), 2003 (DARPA (Defense Advanced Research Projects Agency) funded project)
• (with D.M. Healy and I. Konstantinidis) Wavelet transform for anisotropic diffusion modeling in image processing, Part I.   Preprint.
  
• Wave-imaging software
• (with Harris Wong) Facet Modeling of 2D Equilibrium Crystals. Technical report.
• Facet modeling for 2D equilibrium crystal solid film, 2004 (CCT (Center for Computaton and Technology) funded project).

Links to my review and research papers in American Mathematical Society
and  UC Davis Archiv

 Statistics of science preprints in arXiv