# Alexander A. Kiselev

- William T. Laprade Distinguished Professor of Mathematics
- Professor of Mathematics

##### Links

### Research Areas and Keywords

##### Analysis

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.

### Selected Grants

Small Scale and Singularity Formation in Fluids awarded by National Science Foundation (Principal Investigator). 2020 to 2023

Small Scale and Singularity Formation in Fluid Mechanics and Biology awarded by Simons Foundation (Principal Investigator). 2020 to 2021

Regularity, blow up and mixing in fluids awarded by National Science Foundation (Principal Investigator). 2018 to 2021

### 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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## Pages

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.
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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.

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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 »

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 »

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 »

New Duke professor studies the math of moving fluids https://today.duke.edu/2017/10/alexander-kiselev-mixing-it read more »