Zheng Yuxi

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Zheng Yuxi ( Chinese  郑玉 玺 , Pinyin Zhèng Yùxǐ ; * 1963 in Tancheng County, Shandong Province ) is a Chinese mathematician who lives in the United States . He studies partial differential equations and is a professor at Pennsylvania State University .

Life

Zheng studied at Shandong University from 1979 to 1984 and from 1984 to 1986 at the Institute of Mathematics at Academia Sinica in Beijing . From 1986 he studied at the University of California, Berkeley , where he received his doctorate in 1990 with Ronald DiPerna and Lawrence C. Evans ( Concentration-Cancellation Phenomena for weak solutions to certain nonlinear partial differential equations ). As a post-doctoral student he was at MSRI and at the Institute for Advanced Study in 1991/92 and at the Courant Institute in 1992/93 . In 1993 he became an assistant professor and in 1996 an associate professor at Indiana University . From 2001 he was a professor at Penn State University, with interruptions from 2010 to 2012 as a professor at Yeshiva University . He is the director of the mathematics department at Penn State University.

plant

Zheng continued the work of Andrew Majda and Ronald DiPerna on the global existence of solutions to the two-dimensional Euler equation with vortex initial values ​​(concentration-cancellation method). Majda and DiPerna showed the global existence if the approximate solutions concentrated their energy on a subset of the Hausdorff dimension smaller than 1, Zheng treated the case of dimension 1 and showed global existence if the subset has finite one-dimensional Hausdorff dimension. With Andrew and George Majda he dealt with similar questions in the one-dimensional Vlassov-Poisson equation with measures as initial values.

He also studied wave solutions in liquid crystals , with a combination of numerical and mathematical analysis, where he showed the formation of singularities in finite time.

Zheng was one of the first to investigate Riemann problems in two dimensions instead of in one dimension, as was customary until then, for example in equations of gas dynamics with Tong Zhang. They found exact spiral-vortex-like solutions (similar to hurricanes in the weather). During these investigations a new type of singularity (Delta Shock Waves) emerged.

Honors

In 2007 he gave the DiPerna lecture (Multidimensional systems of conservation laws). From 1995 to 1997 he was a Sloan Research Fellow .

Fonts

  • Systems of conservation laws: two-dimensional Riemann problems . Birkhäuser 2001

Web links

Individual evidence

  1. ↑ http://www.math.psu.edu/yzheng/bvita.html
  2. ↑ Zheng Concentration Cancellation for the Velocity Fields of Two Dimensional Incompressible Fluid Flows , Communications in Mathematical Physics, 135, 1991, pp. 581-594
  3. ↑ Majda, Majda, Zheng Concentrations in the One-Dimensional Vlasov-Poisson Equations , 1,2, Physica D, 74, 1994, 268-300, D 79, 1994, 41-76
  4. ↑ with Robert Glassey, John Hunter Singularities of a Variational Wave Equation , Journal of Differential Equations, 129, 1996, pp. 49-78
  5. ^ Tong Zhang, Zheng Two-dimensional Riemann Problem for a Single Conservation Law , Transactions of the American Mathematical Society, 312, 1989, 589-619
  6. ↑ Zhang, Zheng Riemann Problem for Gasdynamic Combustion , Journal of Differential Equations, 77, 1989, pp. 203-230
  7. ^ Zhang, Zheng Conjecture on Structure of Solutions of Riemann Problem for 2-D Gasdynamic Systems , SIAM Journal on Mathematical Analysis, 21, 1990, pp. 593-630
  8. ^ Zhang, Zheng Exact Spiral Solutions of the Two Dimensional Euler Equations , Discrete and Continuous Dynamical Systems, 3, 1997, pp. 117--133
  9. ↑ DiPerna Lecture 2007
Note: This article places the family name before the person's first name. This is the usual order in Chinese. Zheng is the family name here, Yuxi is the first name.
personal data
SURNAME Zheng, Yuxi
ALTERNATIVE NAMES 郑玉 玺
BRIEF DESCRIPTION Chinese mathematician in the USA
DATE OF BIRTH 1963