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Elling, Volker

Elling, Volker

Research Fellow and Deputy Director

Research Fields: Partial Differential Equations, Fluid Dynamics,


Email : velling@math.sinica.edu.tw

Extension : 741

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.

  • Ph.D. (SCCM) Stanford University 2005/1
  • Diplom (Mathematics) RWTH Aachen 2000/9
  • M.Sc. (Computer Science) Georgia Institute of Technology 1998/9

  • 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

  • 2022-2024, Academia Sinica Presidential Scholar
  • 2021-04, MOST Outstanding Research Award

  • "Convexity of shock polars", (under review), 2023
  • "Shock polars for non-polytropic compressible potential flow", Communications on Pure and Applied Analysis, 21 (5), 1581-1594, 2022-05 , Link
  • "Barotropic Euler shock polars", Zeitschrift für angewandte Mathematik und Physik, 73, 67-, 2022, Link
  • "Van der Waals shock polars with multiple or supersonic critical points", Physics of Fluids, 34, 36110-, 2022, Link
  • "Shock polars for ideal and non-ideal gases", Journal of Fluid Mechanics, 916, 0-, 2021-06 , Link
  • "Vortex cusps", Journal of Fluid Mechanics, 882, 0-, 2020, Link
  • "Triple points and sign of circulation", Physics of Fluids, 31 (12), 126106-, 2019, Link
  • "Piecewise analytic bodies in subsonic potential flow", Communications in Partial Differential Equations, 44 (8), 691-707, 2019, Link
  • (with Manuel V. Gnann) "Variety of unsymmetric multibranched logarithmic vortex spirals", European Journal of Applied Mathematics, 30 (1), 23-38, 2019, Link
  • "Nonexistence of compressible irrotational inviscid flows along infinite protruding corners", Zeitschrift fuer Angewandte Mathematik und Physik, 69 (59), 2018, Link, Link
  • "Subsonic irrotational flow around certain bodies with two protruding corners", Communications on Pure and Applied Analysis, 17 (2), 539-555, 2018, Link, Link
  • "Nonexistence of low-Mach irrotational inviscid flows around polygons", Journal of Differential Equations, 262 (11), 2705-2721, 2017, Link, Link
  • "Self-similar 2d Euler solutions with mixed-sign vorticity", Communications in Mathematical Physics, 348 (1), 27-68, 2016-11 , Link
  • "Relative entropy and compressible potential flow", Acta Math. Sci. Ser. B Engl. Ed., 35 (4), 763-776, 2015
  • (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
  • "Algebraic spiral solutions of 2d incompressible Euler", J. Differential Equations, 255 (11), 3749-3787, 2013
  • "Hölder continuity and differentiability on converging subsequences", Acta Math. Sci., 32 (1), 75-83, 2012
  • "Non-existence of strong regular reflection in self-similar potential flow", J. Diff. Eqns., 252 (3), 2085-2103, 2012, Link
  • (with Joseph Roberts) "Steady self-similar inviscid flow", SIAM J. Math. Anal., 44 (4), 2344-2371, 2012
  • "Regular reflection in self-similar potential flow and the sonic criterion", Commun. Math. Anal., 8 (2), 22-69, 2010
  • "Counterexamples to the sonic criterion", Arch. Rat. Mech. Anal., 194 (3), 987-1010, 2009-12
  • "The carbuncle phenomenon is incurable", Acta Math. Sci. (ser. B), 29 (6), 1647-1656, 2009
  • "Instability of strong regular reflection and counterexamples to the detachment criterion", SIAM J. Appl. Math., 70 (4), 1330-1340, 2009
  • (with Tai-Ping Liu) "Supersonic flow onto a solid wedge", Comm. Pure Appl. Math., 61 (10), 1347-1448, 2008
  • "A Lax-Wendroff type theorem for unstructured quasiuniform grids", Math. Comp., 76 (257), 251-272, 2007
  • "A possible counterexample to wellposedness of entropy solutions and to Godunov scheme convergence", Math. Comp., 75 (256), 1721-1733, 2006
  • (with Tai-Ping Liu) "The ellipticity principle for selfsimilar polytropic potential flows", J. Hyper. Diff. Eqns., 2 (4), 909-917, 2005, Link
  • (with B. Plale, G. Eisenhauer, K. Schwan, D. King, V. Martin) "Realizing distributed computational laboratories", 2 (3), 1999
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