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 reactiondiffusion equations and spectral theory of Schredinger operators.
In the past, I have also worked on reactiondiffusion equations and spectral theory of Schredinger operators.
Current Research Interests
Mathematical Fluid Mechanics, Mathematical Biology, ReactionDiffusion 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
 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 WisconsinMadison. 2005  2014
 Associate Professor, University of WisconsinMadison. 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


Awards & Honors
 12th Brooke Benjamin Lecture. Oxford University. 2019
 International Congress of Mathematicians 2018, Invited Speaker, Partial Differential Equations Section. International Mathematical Union. 2017
 Avron Douglis Memorial Lecture. University of Maryland . 2014
 Guggenheim Fellowship. John Simon Guggenheim Foundation . 2012
 Plenary Speaker at AMS sectional meeting. AMS program committee. 2009
 Invited Speaker at International Congress in Mathematical Physics. International Association of Mathematical Physics. 2006
 NSF Career award. NSF. 2002
 Alfred P. Sloan Research Fellowship. A.P. Sloan Foundation . 2001
 Expertise

Subject Headings
 Research

Selected Grants
 Regularity, blow up and mixing in fluids awarded by National Science Foundation 2018  2020

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

Academic Articles
 Do, T, Kiselev, A, and Xu, X. "Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation." Journal of Nonlinear Science 28, no. 6 (December 2018): 21272152. Full Text
 Kiselev, A. "Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics." Journal of Nonlinear Science 28, no. 6 (December 2018): 20472050. Full Text
 Do, T, Kiselev, A, Ryzhik, L, and Tan, C. "Global Regularity for the Fractional Euler Alignment System." Archive for Rational Mechanics and Analysis 228, no. 1 (April 2018): 137. Full Text Open Access Copy
 Kiselev, A, and Tan, C. "Finite time blow up in the hyperbolic Boussinesq system." Advances in Mathematics 325 (February 2018): 3455. Full Text
 Kiselev, A, and Tan, C. "Global Regularity for 1D Eulerian Dynamics with Singular Interaction Forces." Siam Journal on Mathematical Analysis 50, no. 6 (January 2018): 62086229. Full Text Open Access Copy
 Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "On the FiniteTime Blowup of a OneDimensional Model for the ThreeDimensional Axisymmetric Euler Equations." Communications on Pure and Applied Mathematics 70, no. 11 (November 2017): 22182243. 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): 12531315. 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): 909948. Full Text
 Kiselev, A, and Xu, X. "Suppression of Chemotactic Explosion by Mixing." Archive for Rational Mechanics and Analysis 222, no. 2 (November 2016): 10771112. 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): 782788. 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): 34903494. 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): 16671679. Full Text
 Kiselev, A, and Šverák, V. "Small scale creation for solutions of the incompressible twodimensional Euler equation." Annals of Mathematics (November 1, 2014): 12051220. Full Text
 Iyer, G, Kiselev, A, and Xu, X. "Lower bounds on the mix norm of passive scalars advected by incompressible enstrophyconstrained flows." Nonlinearity 27, no. 5 (May 1, 2014): 973985. 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): 115609115609. Full Text
 Dabkowski, M, Kiselev, A, and Vicol, V. "Global wellposedness for a slightly supercritical surface quasigeostrophic equation." Nonlinearity 25, no. 5 (May 1, 2012): 15251535. 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): 298318. Full Text
 Kiselev, A, and Nazarov, F. "A Simple Energy Pump for the Surface Quasigeostrophic Equation." (2012): 175179. Full Text
 Kiselev, A. "Nonlocal maximum principles for active scalars." Advances in Mathematics 227, no. 5 (August 2011): 18061826. Full Text
 Kiselev, A, and Nazarov, F. "Variation on a theme of caffarelli and vasseur." Journal of Mathematical Sciences 166, no. 1 (April 2010): 3139. Full Text
 Kiselev, A, and Nazarov, F. "Global regularity for the critical dispersive dissipative surface quasigeostrophic equation." Nonlinearity 23, no. 3 (March 1, 2010): 549554. 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): 3165. Full Text
 Kiselev, A. "Regularity and Blow up for Active Scalars." Mathematical Modelling of Natural Phenomena 5, no. 4 (2010): 225255. 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): 552568. 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): 643674. Full Text
 "Blow up and regularity for fractal burgers equation." Dynamics of Partial Differential Equations 5, no. 3 (January 1, 2008): 211240. Full Text
 Kiselev, A, Shterenberg, R, and Zlatos, A. "Relaxation enhancement by timeperiodic flows." Indiana University Mathematics Journal 57, no. 5 (2008): 21372152. Full Text
 Kiselev, A, Nazarov, F, and Volberg, A. "Global wellposedness for the critical 2D dissipative quasigeostrophic equation." Inventiones Mathematicae 167, no. 3 (March 1, 2007): 445453. (Review) 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): 565589. Link to Item
 Kiselev, A, and Zlatoš, A. "Quenching of combustion by shear flows." Duke Mathematical Journal 132, no. 1 (March 2006): 4972. 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): 4069. Full Text
 Andrzejewski, D, Butzlaff, E, Kiselev, A, and Markely, LRA. "Enhancement of combustion by drift in a coupled reactiondiffusion model." Communications in Mathematical Sciences 4, no. 1 (2006): 213225. Full Text
 "Quenching and propagation in KPP reactiondiffusion equations with a heat loss." Archive for Rational Mechanics and Analysis 178, no. 1 (October 1, 2005): 5780. Full Text
 "On discrete models of the Euler equation." International Mathematics Research Notices , no. 38 (August 28, 2005): 23152339. (Review)
 Kiselev, A. "Imbedded singular continuous spectrum for Schrödinger operators." Journal of the American Mathematical Society 18, no. 3 (July 1, 2005): 571603. 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): 787830. Full Text
 "Fronts in Reactive Convection: Bounds, Stability, and Instability." Communications on Pure and Applied Mathematics 56, no. 12 (December 1, 2003): 17811803. 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): 487508. Full Text
 Christ, M, and Kiselev, A. "Absolutely continuous spectrum of Stark operators." Arkiv För Matematik 41, no. 1 (April 2003): 133. 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): 127. Full Text
 Killip, R, Kiselev, A, and Last, Y. "Dynamical upper bounds on wavepacket spreading." American Journal of Mathematics 125, no. 5 (2003): 11651198. Full Text
 Christ, M, and Kiselev, A. "Scattering and Wave Operators for OneDimensional Schr�dinger Operators with Slowly Decaying Nonsmooth Potentials." Geometrical and Functional Analysis Gafa 12, no. 6 (December 2002): 11741234. Full Text
 Gesztesy, F, Kiselev, A, and Makarov, KA. "Uniqueness Results for MatrixValued Schrödinger, Jacobi, and DiracType Operators." Mathematische Nachrichten 239240, no. 1 (June 2002): 103145. 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): 13201342. Full Text
 Kiselev, A, and Ryzhik, L. "An upper bound for the bulk burning rate for systems." Nonlinearity 14, no. 5 (September 1, 2001): 12971310. Full Text
 Kiselev, A, and Ryzhik, L. "Enhancement of the traveling front speeds in reactiondiffusion equations with advection." Annales De L'Institut Henri Poincare (C) Non Linear Analysis 18, no. 3 (May 2001): 309358. Full Text
 Christ, M, and Kiselev, A. "WKB and Spectral Analysis¶of OneDimensional Schrödinger Operators¶with Slowly Varying Potentials." Communications in Mathematical Physics 218, no. 2 (April 2001): 245262. Full Text
 Christ, M, and Kiselev, A. "WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for OneDimensional Schrödinger Operators with Slowly Decaying Potentials." Journal of Functional Analysis 179, no. 2 (February 2001): 426447. Full Text
 Christ, M, and Kiselev, A. "Maximal functions associated to filtrations." Journal of Functional Analysis 179, no. 2 (February 1, 2001): 409425. Full Text
 Kiselev, A. "Absolutely continuous spectrum of perturbed stark operators." Transactions of the American Mathematical Society 352, no. 1 (December 1, 2000): 243256.
 "Solutions, spectrum, and dynamics for schrödinger operators on infinite domains." Duke Mathematical Journal 102, no. 1 (January 1, 2000): 125150. Full Text
 "Bulk burning rate in passivereactive diffusion." Archive for Rational Mechanics and Analysis 154, no. 1 (January 1, 2000): 5391. 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): 17811785.
 Kiselev, A, Remling, C, and Simon, B. "Effective Perturbation Methods for OneDimensional Schrödinger Operators." Journal of Differential Equations 151, no. 2 (January 1999): 290312. Full Text
 Christ, M, and Kiselev, A. "Absolutely continuous spectrum for onedimensional Schrödinger operators with slowly decaying potentials: Some optimal results." Journal of the American Mathematical Society 11, no. 4 (October 1, 1998): 771797.
 Kiselev, A. "and a.e. convergence of integral operators." Duke Mathematical Journal 94, no. 3 (September 1998): 619646. Full Text
 Kiselev, A, Last, Y, and Simon, B. "Modified Prüfer and EFGP Transforms and the Spectral Analysis of OneDimensional Schrödinger Operators." Communications in Mathematical Physics 194, no. 1 (May 1, 1998): 145. Full Text
 Kiselev, A. "Some Examples in OneDimensional “Geometric” Scattering on Manifolds." Journal of Mathematical Analysis and Applications 212, no. 1 (August 1997): 263280. Full Text
 Christ, M, Kiselev, A, and Remling, C. "The absolutely continuous spectrum of onedimensional Schrödinger operators with decaying potentials." Mathematical Research Letters 4, no. 5 (1997): 719723. Full Text
 Kiselev, A. "Absolutely continuous spectrum of onedimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials." Communications in Mathematical Physics 179, no. 2 (August 1996): 377399. 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): 12761285. Full Text
 Kiselev, A, and Simon, B. "Rank One Perturbations with Infinitesimal Coupling." Journal of Functional Analysis 130, no. 2 (June 1995): 345356. Full Text
 Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "On the FiniteTime Blowup of a 1D Model for the 3D Axisymmetric Euler Equations." Link to Item
 Dabkowski, M, Kiselev, A, Silvestre, L, and Vicol, V. "Global wellposedness of slightly supercritical active scalar equations(Published online)." Analysis & Pde 7, no. 1: 4372. Full Text
 Kiselev, A, and Li, C. "Global Regularity and Fast Small Scale Formation for Euler Patch Equation in a Smooth Domain." . Link to Item
 Kiselev, A, and Ryzhik, L. "A simple model for asset price bubble formation and collapse."
 Kiselev, A, and Yang, H. "Analysis of a Singular Boussinesq Model." . Link to Item

Conference Papers
 Kiselev, A. "Some recent results on the critical surface quasigeostrophic equation: A review." 2009. Link to Item
 Kiselev, A. "Diffusion and Mixing in Fluid Flow: A Review." : Springer Netherlands, 2009. Full Text

 Teaching & Mentoring

Recent Courses

Advising & Mentoring

I am currently advising two graduate students (Hang Yang and Yishu Gong) and one postdoctoral fellow (Siming He). One of my graduate students, Chao Li, got his PhD this year (from Rice) and moved on to a position at Goldman Sachs. A postdoctoral fellow I mentored, Changhui Tan, moved on to a tenure track position at University of South Carolina this year.
I also serve as an advisor to two undergraduate students, Amy Fan and Adam York, and I serve this year as a teaching mentor to postdoctoral fellow Nan Wu.

I am currently advising two graduate students (Hang Yang and Yishu Gong) and one postdoctoral fellow (Siming He). One of my graduate students, Chao Li, got his PhD this year (from Rice) and moved on to a position at Goldman Sachs. A postdoctoral fellow I mentored, Changhui Tan, moved on to a tenure track position at University of South Carolina this year.
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Small scale creation in fluids. Analysis seminar. Kent University. November 2018 2018
 Small scale creation in fluids. Colloquium. University of Toronto. November 2018 2018
 Small scale creation in fluids. 82nd Midwest PDE seminar. October 2018 2018
 Enhancement of reactions by chemotaxis. Banff International Research Station. August 2018 2018
 Intorduction to Fluids. Summer Workshop in Math (SWiM). Duke University. June 2018 2018
 Small scale creation in fluids. Workshop on Mathematical fine structures in fluid dynamics. Gran Sasso Science Institute, l'Aquila, Italy. June 2018  June 2018 2018
 Growth in solutions of 2D Euler equation. Colloquium. UCSD. April 2018 2018
 Small Scale and Singularity Formation in Fluid Mechanics . SIAM conference on Partial Differential Equations. December 2017 2017
 Suppression of chemotactic explosion by fluid flow . SIAM conference on Partial Differential Equations. December 2017 2017
 Regularity Properties of Euler Alignment System. ReactionDiffusion, Propagation, and Modelling. Institut Henri Poincare. November 2017 2017
 Small scale creation in solutions of the 2D Euler equation . Analysis seminar. UNC Chapel Hill . October 2017 2017
 Regularity and Blow Up for Active Scalars. Analysis seminar. Princeton University. September 2017 2017
 Small scale creation in solutions of the 2D Euler equation . PDE seminar. Georgia Tech . September 2017 2017
 Singularity Formation in Models of Fluid Mechanics. Summer school: Various Aspects of Mathematical Physics. Euler Institute . July 2017 2017
 Singularity formation in modified SQG patches. Workshop Irregular transport: analysis and applications. University of Basel. July 2017 2017
 Regularity and Blow Up for Active Scalars. Summer School and Workshop: Mathematical Analysis of Water Waves and Related Models. UC Davis. June 2017 2017
 Enhancement of Biological Reactions by Chemotaxis . Colloquium. University of Miami. April 2017 2017
 Small scale creation in solutions of the 2D Euler equation . Colloquium. USC. March 2017 2017

Service to the Profession
 Coordinating Editor. Memoirs of the AMS. January 2019 2019
 Coordinating Editor. Transactions of the AMS. January 2019 2019
 Associate Editor, Dynamics of PDE. September 2017 2017
 Editorial Board, Nonlinearity. January 2017 2017
 Editorial Board, Memoirs of the AMS. January 2013 2013
 Editorial Board, Transactions of the AMS. January 2013 2013
 Associate Editor, Communications in Mathematical Sciences. January 2011 2011

Service to Duke
 Appointments. 2018  2019 2018  2019
 Appointments. 2017  2018 2017  2018
 Postdoctoral Appointments. 2017  2018 2017  2018
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