# Alexander A. Kiselev

### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### Mathematical Physics

##### PDE & Dynamical Systems

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

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 Li, C. "Global regularity and fast small-scale formation for Euler patch equation in a smooth domain(Accepted)." *Communications in Partial Differential Equations* (January 1, 2019).
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Do, T, Kiselev, A, and Xu, X. "Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation." *Journal of Nonlinear Science* 28.6 (December 1, 2018): 2127-2152.
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Kiselev, A. "Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics." *Journal of Nonlinear Science* 28.6 (December 1, 2018): 2047-2050.
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Do, T, Kiselev, A, Ryzhik, L, and Tan, C. "Global Regularity for the Fractional Euler Alignment System." *Archive for Rational Mechanics and Analysis* 228.1 (April 1, 2018).
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Kiselev, A, and Tan, C. "Finite time blow up in the hyperbolic Boussinesq system." *Advances in Mathematics* 325 (February 5, 2018): 34-55.
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Kiselev, A, and Tan, C. "Global regularity for 1D eulerian dynamics with singular interaction forces." *Siam Journal on Mathematical Analysis* 50.6 (January 1, 2018): 6208-6229.
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Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations." *Communications on Pure and Applied Mathematics* 70.11 (November 1, 2017): 2218-2243.
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Kiselev, A, Yao, Y, and Zlatoš, A. "Local Regularity for the Modified SQG Patch Equation." *Communications on Pure and Applied Mathematics* 70.7 (July 1, 2017): 1253-1315.
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Kiselev, A, and Xu, X. "Suppression of Chemotactic Explosion by Mixing." *Archive for Rational Mechanics and Analysis* 222.2 (November 1, 2016): 1077-1112.
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Popov, I, Kurasov, P, Naboko, S, Kiselev, A, Ryzhkov, A, Yafyasov, A, Miroshnichenko, G, Karpeshina, Y, Kruglov, V, Pankratova, T, and Popov, A. "A distinguished mathematical physicist Boris S. Pavlov." *Nanosystems: Physics, Chemistry, Mathematics* (October 25, 2016): 782-788.
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## Pages

Kiselev, A. "Some recent results on the critical surface quasi-geostrophic equation: A review." 2009.

Kiselev, A. "Diffusion and Mixing in Fluid Flow: A Review.": Springer Netherlands, 2009. Full Text

## Pages

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 »