Alexander A. Kiselev

Alexander A. Kiselev
  • William T. Laprade Distinguished Professor of Mathematics
  • Professor of Mathematics

Research Areas and Keywords


Fourier analysis, functional analysis

Biological Modeling

Chemotaxis, enhancement of biological reactions

Mathematical Physics

Spectral theory, Schrodinger operators

PDE & Dynamical Systems

Fluid mechanics, Euler equation, surface quasi-geostrophic equation, singularity formation, small scale creation, mixing efficiency

My current research interests focus on mathematical fluid mechanics and mathematical biology.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators. 

Education & Training
  • Ph.D., California Institute of Technology 1997

Selected Grants

Regularity, blow up and mixing in fluids awarded by National Science Foundation (Principal Investigator). 2018 to 2020

Fellowships, Supported Research, & Other Grants

Regularity, Blow UP, and Mixing in Fluids awarded by NSF (2017 to 2020)

Topics in Applied PDE awarded by NSF (2014 to 2018)

Kiselev, A., and C. Li. “Global regularity and fast small-scale formation for Euler patch equation in a smooth domain.” Communications in Partial Differential Equations, vol. 44, no. 4, Apr. 2019, pp. 279–308. Scopus, doi:10.1080/03605302.2018.1546318. Full Text

Do, T., et al. “Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation.” Journal of Nonlinear Science, vol. 28, no. 6, Dec. 2018, pp. 2127–52. Scopus, doi:10.1007/s00332-016-9340-7. Full Text

Kiselev, A. “Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics.” Journal of Nonlinear Science, vol. 28, no. 6, Dec. 2018, pp. 2047–50. Scopus, doi:10.1007/s00332-018-9452-3. Full Text

Do, T., et al. “Global Regularity for the Fractional Euler Alignment System.” Archive for Rational Mechanics and Analysis, vol. 228, no. 1, Apr. 2018. Scopus, doi:10.1007/s00205-017-1184-2. Full Text Open Access Copy

Kiselev, A., and C. Tan. “Finite time blow up in the hyperbolic Boussinesq system.” Advances in Mathematics, vol. 325, Feb. 2018, pp. 34–55. Scopus, doi:10.1016/j.aim.2017.11.019. Full Text

Kiselev, A., and C. Tan. “Global regularity for 1D eulerian dynamics with singular interaction forces.” Siam Journal on Mathematical Analysis, vol. 50, no. 6, Jan. 2018, pp. 6208–29. Scopus, doi:10.1137/17M1141515. Full Text Open Access Copy

Choi, K., et al. “On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations.” Communications on Pure and Applied Mathematics, vol. 70, no. 11, Nov. 2017, pp. 2218–43. Scopus, doi:10.1002/cpa.21697. Full Text

Kiselev, A., et al. “Local Regularity for the Modified SQG Patch Equation.” Communications on Pure and Applied Mathematics, vol. 70, no. 7, July 2017, pp. 1253–315. Scopus, doi:10.1002/cpa.21677. Full Text

Kiselev, A., and X. Xu. “Suppression of Chemotactic Explosion by Mixing.” Archive for Rational Mechanics and Analysis, vol. 222, no. 2, Nov. 2016, pp. 1077–112. Scopus, doi:10.1007/s00205-016-1017-8. Full Text

Popov, I. Y., et al. “A distinguished mathematical physicist Boris S. Pavlov.” Nanosystems: Physics, Chemistry, Mathematics, ITMO University, Oct. 2016, pp. 782–88. Crossref, doi:10.17586/2220-8054-2016-7-5-782-788. Full Text


Kiselev, Alexander. “Some recent results on the critical surface quasi-geostrophic equation: A review.” Hyperbolic Problems: Theory, Numerics and Applications, Part 1, edited by E. Tadmor et al., vol. 67, AMER MATHEMATICAL SOC, 2009, pp. 105–22.

Kiselev, Alexander. Diffusion and Mixing in Fluid Flow: A Review. Springer Netherlands, 2009, pp. 357–69. Crossref, doi:10.1007/978-90-481-2810-5_24. Full Text

Alexander (Sasha) Kiselev

Congratulations to Duke Mathematics Professor Alexander (Sasha) Kiselev for being named one of the 2020 Simons Fellows in Mathematics and Theoretical Physics.  The Simons Foundation’s... read more »

Euler Tea

The complicated currents in a cup of tea inspired a series of important proofs.  Alexander Kiselev, a mathematician at Duke University and a coauthor of one of the proofs,... read more »

Kiselev Reed Tarokh

Only ten professors were named Distinguished Professors this year in the Trinity College of Arts and Sciences.  This distinction is given to professors for their outstanding research and teaching accomplishments.  We are proud to announce that three... read more »