# Alexander A. Kiselev

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.

### 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 Tan, C. "Finite time blow up in the hyperbolic Boussinesq system." *Advances in Mathematics* 325 (February 5, 2018): 34-55.
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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 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 2017): 1253-1315.
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Kiselev, A, Ryzhik, L, Yao, Y, and Zlatoš, A. "Finite time singularity for the modified SQG patch equation." *Annals of Mathematics* 184.3 (November 1, 2016): 909-948.
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Kiselev, A, and Xu, X. "Suppression of Chemotactic Explosion by Mixing." *Archive for Rational Mechanics and Analysis* 222.2 (November 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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Kiselev, A, and Zlatoš, A. "Blow up for the 2D Euler equation on some bounded domains." *Journal of Differential Equations* 259.7 (October 2015): 3490-3494.
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Choi, K, Kiselev, A, and Yao, Y. "Finite Time Blow Up for a 1D Model of 2D Boussinesq System." *Communications in Mathematical Physics* 334.3 (March 2015): 1667-1679.
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Kiselev, A, and Šverák, V. "Small scale creation for solutions of the incompressible two-dimensional Euler equation." *Annals of Mathematics* (November 1, 2014): 1205-1220.
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Iyer, G, Kiselev, A, and Xu, X. "Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows." *Nonlinearity* 27.5 (May 1, 2014): 973-985.
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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." 2009. Full Text

## Pages

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