中央研究院
　數學研究所
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研究員 兼副所長 |   艾沃克
聯絡資訊
  • velling$\color{red}{@}$math.sinica.edu.tw
  • +886 2 2368-5999 ext. 741
  • +886 2 2368-9771
研究專長
  • 偏微分方程
  • 流體動力學
學歷
  • Ph.D. (SCCM) Stanford University (2005/1)
  • Diplom (Mathematics) RWTH Aachen (2000/9)
  • M.Sc. (Computer Science) Georgia Institute of Technology (1998/9)
相關連結
經歷
  • Associate Professor (with tenure) Univ. of Michigan 2012/9 - 2017/6
  • Assistant Professor (tenure-track) Univ. of Michigan 2007/9 - 2012/9
  • Prager Assistant Professor (postdoc) Brown Univ. 2005/6 - 2007/9
  • Postdoctoral researcher Stanford Univ. 2005/1 - 2005/6
獲獎
  • MOST Outstanding Research Award, 2021-04
研究簡介

Dr. Elling's research interests are in partial differential equations 
 modelling fluid dynamics. His past work focuses on shock reflection,
 in particular weak-strong selection and regular-Mach transition, 
 on non-uniqueness and the carbuncle phenomenon, and more recently 
 on existence of vortex spirals in incompressible flow.

部分著作目錄
  1. "Shock polars for non-polytropic compressible potential flow" , Communications on Pure and Applied Analysis , 21 (5), 1581-1594, 2022-05. (https://www.aimsciences.org/article/doi/10.3934/cpaa.2022032)
  2. "Barotropic Euler shock polars" , Zeitschrift für angewandte Mathematik und Physik , 73, 67-, 2022.
  3. "Van der Waals shock polars with multiple or supersonic critical points" , Physics of Fluids , 34, 036110-, 2022.
  4. "Shock polars for ideal and non-ideal gases" , Journal of Fluid Mechanics , 916, A51-, 2021-06. (https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/shock-polars-for-ideal-and-nonideal-gases/E83AC77761426330C1FCBCE04BB83F91)
  5. "Vortex cusps" , Journal of Fluid Mechanics , 882, A17-, 2020. (https://doi.org/10.1017/jfm.2019.827)
  6. "Triple points and sign of circulation" , Physics of Fluids , 31 (12), 126106-, 2019. (https://doi.org/10.1063/1.5122679)
  7. "Piecewise analytic bodies in subsonic potential flow" , Communications in Partial Differential Equations , 44 (8), 691-707, 2019. (https://www.tandfonline.com/doi/full/10.1080/03605302.2019.1597112)
  8. (with Manuel V. Gnann) "Variety of unsymmetric multibranched logarithmic vortex spirals" , European Journal of Applied Mathematics , 30 (1), 23-38, 2019.
  9. "Nonexistence of compressible irrotational inviscid flows along infinite protruding corners" , Zeitschrift fuer Angewandte Mathematik und Physik , 69 (59), 2018. http://arxiv.org/
  10. "Subsonic irrotational flow around certain bodies with two protruding corners" , Communications on Pure and Applied Analysis , 17 (2), 539-555, 2018. http://arxiv.org/
  11. "Nonexistence of low-Mach irrotational inviscid flows around polygons" , Journal of Differential Equations , 262 (11), 2705-2721, 2017. (http://dx.doi.org/10.1016/j.jde.2016.11.014) http://arxiv.org/
  12. "Self-similar 2d Euler solutions with mixed-sign vorticity" , Communications in Mathematical Physics , 348 (1), 27-68, 2016-11.
  13. "Relative entropy and compressible potential flow" , Acta Math. Sci. Ser. B Engl. Ed. , 35 (4), 763-776, 2015.
  14. (with Joseph Roberts) "Steady and Self-Similar Solutions of Non-Strictly Hyperbolic Systems of Conservation Laws" , Communications in Partial Differential Equations , 39 (7), 1364-1392, 2014.
  15. "Algebraic spiral solutions of 2d incompressible Euler" , J. Differential Equations , 255 (11), 3749-3787, 2013.
  16. "Hölder continuity and differentiability on converging subsequences" , Acta Math. Sci. , 32B (1), 75-83, 2012.
  17. "Non-existence of strong regular reflection in self-similar potential flow" , J. Diff. Eqns. , 252 (3), 2085-2103, 2012.
  18. (with Joseph Roberts) "Steady self-similar inviscid flow" , SIAM J. Math. Anal. , 44 (4), 2344-2371, 2012.
  19. "Regular reflection in self-similar potential flow and the sonic criterion" , Commun. Math. Anal. , 8 (2), 22-69, 2010.
  20. "Counterexamples to the sonic criterion" , Arch. Rat. Mech. Anal. , 194 (3), 987-1010, 2009-12.
  21. "The carbuncle phenomenon is incurable" , Acta Math. Sci. (ser. B) , 29 (6), 1647-1656, 2009.
  22. "Instability of strong regular reflection and counterexamples to the detachment criterion" , SIAM J. Appl. Math. , 70 (4), 1330-1340, 2009.
  23. (with Tai-Ping Liu) "Supersonic flow onto a solid wedge" , Comm. Pure Appl. Math. , 61 (10), 1347-1448, 2008.
  24. "A Lax-Wendroff type theorem for unstructured quasiuniform grids" , Math. Comp. , 76 (257), 251-272, 2007.
  25. "A possible counterexample to wellposedness of entropy solutions and to Godunov scheme convergence" , Math. Comp. , 75 (256), 1721-1733, 2006.
  26. (with Tai-Ping Liu) "The ellipticity principle for selfsimilar polytropic potential flows" , J. Hyper. Diff. Eqns. , 2 (4), 909-917, 2005. (https://www.worldscientific.com/doi/abs/10.1142/S0219891605000646)
  27. (with B. Plale, G. Eisenhauer, K. Schwan, D. King, V. Martin) "Realizing distributed computational laboratories" , 2 (3), 1999.
所長及副所長