Alexander A. Kiselev | Scholars@Duke

Alexander A. Kiselev
William T. Laprade Professor of Mathematics

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.

Current Research Interests

Mathematical Fluid Mechanics, Mathematical Biology, Reaction-Diffusion equations, Spectral theory of Schredinger operators

Current Appointments & Affiliations

William T. Laprade Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018
Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2017

Contact Information

kiselev@math.duke.edu

Background
Education, Training, & Certifications
- Ph.D., California Institute of Technology 1997
Academic Positions Outside Duke
- Edgar Odell Lovett Professor of Mathematics, Rice University. 2017
- Professor, Rice University. 2014 - 2016
- Professor, University of Wisconsin-Madison. 2005 - 2014
- Associate Professor, University of Wisconsin-Madison. 2002 - 2005
- Assistant Professor, University of Chicago. 1999 - 2002
- Dickson Instructor , University of Chicago. 1997 - 1999
- Postdoc, Mathematical Sciences Research Institute. 1996 - 1997
Recognition
In the News
- OCT 5, 2017
  
  Alexander Kiselev: Mixing It Up
Awards & Honors
Expertise
Subject Headings
Research
Fellowships, Supported Research, & Other Grants
- Regularity, Blow UP, and Mixing in Fluids awarded by NSF 2017 - 2020
- Topics in Applied PDE awarded by NSF 2014 - 2018
Publications & Artistic Works
Selected Publications
- Conference Papers
  - Kiselev, A. "Some recent results on the critical surface quasi-geostrophic equation: A review." 2009. Link to Item
  - Kiselev, A. "Diffusion and Mixing in Fluid Flow: A Review." 2009. Full Text Link to Item
- Journal Articles
  - Kiselev, A, and Tan, C. "Finite time blow up in the hyperbolic Boussinesq system." Advances in Mathematics 325 (February 5, 2018): 34-55. Full Text
  - 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, no. 11 (November 2017): 2218-2243. Full Text
  - Kiselev, A, Yao, Y, and Zlatoš, A. "Local Regularity for the Modified SQG Patch Equation." Communications on Pure and Applied Mathematics 70, no. 7 (July 2017): 1253-1315. Full Text
  - Kiselev, A, Ryzhik, L, Yao, Y, and Zlatoš, A. "Finite time singularity for the modified SQG patch equation." Annals of Mathematics 184, no. 3 (November 1, 2016): 909-948. Full Text
  - Kiselev, A, and Xu, X. "Suppression of Chemotactic Explosion by Mixing." Archive for Rational Mechanics and Analysis 222, no. 2 (November 2016): 1077-1112. Full Text
  - 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. Full Text
  - Kiselev, A, and Zlatoš, A. "Blow up for the 2D Euler equation on some bounded domains." Journal of Differential Equations 259, no. 7 (October 2015): 3490-3494. Full Text
  - Choi, K, Kiselev, A, and Yao, Y. "Finite Time Blow Up for a 1D Model of 2D Boussinesq System." Communications in Mathematical Physics 334, no. 3 (March 2015): 1667-1679. Full Text
  - 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. Full Text
  - Iyer, G, Kiselev, A, and Xu, X. "Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows." Nonlinearity 27, no. 5 (May 1, 2014): 973-985. Full Text
  - Dabkowski, M, Kiselev, A, Silvestre, L, and Vicol, V. "Global well-posedness of slightly supercritical active scalar equations." Analysis & PDE 7, no. 1 (2014): 43-72. Full Text
  - Kiselev, A, and Nazarov, F. "A simple energy pump for the surface quasi-geostrophic equation." Nonlinear Partial Differential Equations: The Abel Symposium 2010 (December 1, 2012): 175-179. Full Text
  - Kiselev, A, and Ryzhik, L. "Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case." Journal of Mathematical Physics 53, no. 11 (November 2012): 115609-115609. Full Text
  - Dabkowski, M, Kiselev, A, and Vicol, V. "Global well-posedness for a slightly supercritical surface quasi-geostrophic equation." Nonlinearity 25, no. 5 (May 1, 2012): 1525-1535. Full Text
  - Kiselev, A, and Ryzhik, L. "Biomixing by Chemotaxis and Enhancement of Biological Reactions." Communications in Partial Differential Equations 37, no. 2 (February 2012): 298-318. Full Text
  - Kiselev, A. "Nonlocal maximum principles for active scalars." Advances in Mathematics 227, no. 5 (August 2011): 1806-1826. Full Text
  - Kiselev, A, and Nazarov, F. "Variation on a theme of caffarelli and vasseur." Journal of Mathematical Sciences 166, no. 1 (April 2010): 31-39. Full Text
  - Kiselev, A, and Nazarov, F. "Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation." Nonlinearity 23, no. 3 (March 1, 2010): 549-554. Full Text
  - Berestycki, H, Kiselev, A, Novikov, A, and Ryzhik, L. "The explosion problem in a flow." Journal d'Analyse Mathématique 110, no. 1 (January 2010): 31-65. Full Text
  - Kiselev, A. "Regularity and Blow up for Active Scalars." Mathematical Modelling of Natural Phenomena 5, no. 4 (2010): 225-255. Full Text
  - Kim, A, and Kiselev, A. "Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials." Mathematische Nachrichten 282, no. 4 (April 2009): 552-568. Full Text
  - Constantin, P, Kiselev, A, Ryzhik, L, and Zlatoš, A. "Diffusion and mixing in fluid flow." Annals of Mathematics 168, no. 2 (September 1, 2008): 643-674. Full Text
  - Kiselev, A, Nazarov, F, and Shterenberg, R. "Blow up and regularity for fractal Burgers equation." Dynamics of Partial Differential Equations 5, no. 3 (2008): 211-240. Full Text
  - Kiselev, A, Shterenberg, R, and Zlatos, A. "Relaxation enhancement by time-periodic flows." Indiana University Mathematics Journal 57, no. 5 (2008): 2137-2152. Full Text
  - Kiselev, A, Nazarov, F, and Volberg, A. "Global well-posedness for the critical 2D dissipative quasi-geostrophic equation." Inventiones mathematicae 167, no. 3 (January 27, 2007): 445-453. Full Text
  - Denisov, SA, and Kiselev, A. "Spectral properties of schrodinger operators with decaying potentials." Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday 76 (2007): 565-589. Link to Item
  - Kiselev, A, and Zlatoš, A. "Quenching of combustion by shear flows." Duke Mathematical Journal 132, no. 1 (March 2006): 49-72. Full Text
  - Fannjiang, A, Kiselev, A, and Ryzhik, L. "Quenching of reaction by cellular flows." GAFA Geometric And Functional Analysis 16, no. 1 (February 2006): 40-69. Full Text
  - Andrzejewski, D, Butzlaff, E, Kiselev, A, and Markely, LRA. "Enhancement of combustion by drift in a coupled reaction-diffusion model." Communications in Mathematical Sciences 4, no. 1 (2006): 213-225. Full Text
  - Berestycki, H, Hamel, F, Kiselev, A, and Ryzhik, L. "Quenching and Propagation in KPP Reaction-Diffusion Equations with a Heat Loss." Archive for Rational Mechanics and Analysis 178, no. 1 (October 2005): 57-80. Full Text
  - Kiselev, A, and Zlatoš, A. "On discrete models of the Euler equation." International Mathematics Research Notices , no. 38 (August 28, 2005): 2315-2339. (Review)
  - Kiselev, A. "Imbedded singular continuous spectrum for Schrödinger operators." Journal of the American Mathematical Society 18, no. 3 (July 1, 2005): 571-603. Full Text
  - Germinet, F, Kiselev, A, and Tcheremchantsev, S. "Transfer matrices and transport for Schrödinger operators." Annales de l’institut Fourier 54, no. 3 (2004): 787-830. Full Text
  - Constantin, P, Kiselev, A, and Ryzhik, L. "Fronts in reactive convection: Bounds, stability, and instability." Communications on Pure and Applied Mathematics 56, no. 12 (December 2003): 1781-1803. Full Text
  - Vladimirova, N, Constantin, P, Kiselev, A, Ruchayskiy, O, and Ryzhik, L. "Flame enhancement and quenching in fluid flows." Combustion Theory and Modelling 7, no. 3 (September 2003): 487-508. Full Text
  - Christ, M, and Kiselev, A. "Absolutely continuous spectrum of Stark operators." Arkiv för Matematik 41, no. 1 (April 2003): 1-33. Full Text
  - Kiselev, A, Last, Y, and Simon, B. "Stability of singular spectral types under decaying perturbations." Journal of Functional Analysis 198, no. 1 (February 2003): 1-27. Full Text
  - Killip, R, Kiselev, A, and Last, Y. "Dynamical upper bounds on wavepacket spreading." American Journal of Mathematics 125, no. 5 (2003): 1165-1198. Full Text
  - Christ, M, and Kiselev, A. "Scattering and Wave Operators for One-Dimensional Schr�dinger Operators with Slowly Decaying Nonsmooth Potentials." Geometrical and Functional Analysis GAFA 12, no. 6 (December 2002): 1174-1234. Full Text
  - Gesztesy, F, Kiselev, A, and Makarov, KA. "Uniqueness Results for Matrix-Valued Schrödinger, Jacobi, and Dirac-Type Operators." Mathematische Nachrichten 239-240, no. 1 (June 2002): 103-145. Full Text
  - Constantin, P, Kiselev, A, and Ryzhik, L. "Quenching of flames by fluid advection." Communications on Pure and Applied Mathematics 54, no. 11 (November 2001): 1320-1342. Full Text
  - Kiselev, A, and Ryzhik, L. "An upper bound for the bulk burning rate for systems." Nonlinearity 14, no. 5 (September 1, 2001): 1297-1310. Full Text
  - Kiselev, A, and Ryzhik, L. "Enhancement of the traveling front speeds in reaction-diffusion equations with advection." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 18, no. 3 (May 2001): 309-358. Full Text
  - Christ, M, and Kiselev, A. "WKB and Spectral Analysis¶of One-Dimensional Schrödinger Operators¶with Slowly Varying Potentials." Communications in Mathematical Physics 218, no. 2 (April 2001): 245-262. Full Text
  - Christ, M, and Kiselev, A. "WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials." Journal of Functional Analysis 179, no. 2 (February 2001): 426-447. Full Text
  - Christ, M, and Kiselev, A. "Maximal Functions Associated to Filtrations." Journal of Functional Analysis 179, no. 2 (February 2001): 409-425. Full Text
  - Kiselev, A. "Absolutely continuous spectrum of perturbed stark operators." Transactions of the American Mathematical Society 352, no. 1 (December 1, 2000): 243-256.
  - Constantin, P, Kiselev, A, Oberman, A, and Ryzhik, L. "Bulk Burning Rate in¶Passive–Reactive Diffusion." Archive for Rational Mechanics and Analysis 154, no. 1 (August 2000): 53-91. Full Text
  - Last, Y, and Kiselev, A. "Solutions, spectrum, and dynamics for Schr�dinger operators on infinite domains." Duke Mathematical Journal 102, no. 1 (March 2000): 125-150. Full Text
  - Kiselev, A. "An interpolation theorem related to the A.E. convergence of integral operators." Proceedings of the American Mathematical Society 127, no. 6 (December 1, 1999): 1781-1785.
  - Kiselev, A, Remling, C, and Simon, B. "Effective Perturbation Methods for One-Dimensional Schrödinger Operators." Journal of Differential Equations 151, no. 2 (January 1999): 290-312. Full Text
  - Christ, M, and Kiselev, A. "Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results." Journal of the American Mathematical Society 11, no. 4 (October 1, 1998): 771-797.
  - Kiselev, A. "and a.e. convergence of integral operators." Duke Mathematical Journal 94, no. 3 (September 1998): 619-646. Full Text
  - Kiselev, A, Last, Y, and Simon, B. "Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators." Communications in Mathematical Physics 194, no. 1 (May 1, 1998): 1-45. Full Text
  - Kiselev, A. "Some Examples in One-Dimensional “Geometric” Scattering on Manifolds." Journal of Mathematical Analysis and Applications 212, no. 1 (August 1997): 263-280. Full Text
  - Christ, M, Kiselev, A, and Remling, C. "The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials." Mathematical Research Letters 4, no. 5 (1997): 719-723. Full Text
  - Kiselev, A. "Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials." Communications in Mathematical Physics 179, no. 2 (August 1996): 377-399. Full Text
  - Kiselev, AA, and Popov, IY. "Indefinite metric and scattering by a domain with a small hole." Mathematical Notes 58, no. 6 (December 1995): 1276-1285. Full Text
  - Kiselev, A, and Simon, B. "Rank One Perturbations with Infinitesimal Coupling." Journal of Functional Analysis 130, no. 2 (June 1995): 345-356. Full Text
  - Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations." Link to Item
  - Do, T, Kiselev, A, Ryzhik, L, and Tan, C. "Global Regularity for the Fractional Euler Alignment System (Published online)." Archive for Rational Mechanics and Analysis . Full Text Open Access Copy
  - Do, T, Kiselev, A, and Xu, X. "Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation (Published online)." Journal of Nonlinear Science . Full Text
  - Kiselev, A, and Ryzhik, L. "A simple model for asset price bubble formation and collapse."
  - Kiselev, A, and Tan, C. "Global regularity for 1D Eulerian dynamics with singular interaction forces." Open Access Copy Link to Item
Teaching & Mentoring
Recent Courses
Advising & Mentoring
- I am currently advising three graduate students (Chao Li, Hang Yang and Yishu Gong) and one postdoctoral fellow (Changhui Tan). Yishu Gong is the second year student here at Duke; Hang Yang is visiting here at Duke from Rice. Chao Li is at Rice and expected to graduate in 2018, Changhui Tan finishes his term at Rice in 2018.
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Service to the Profession
Service to Duke
- Appointments. 2017 - 2018 2017 - 2018
- Postdoctoral Appointments. 2017 - 2018 2017 - 2018

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Education, Training, & Certifications

Academic Positions Outside Duke

In the News

Awards & Honors

Subject Headings

Fellowships, Supported Research, & Other Grants

Selected Publications

Conference Papers

Journal Articles

Recent Courses

Advising & Mentoring

Presentations & Appearances

Service to the Profession

Service to Duke