Math @ Duke

Papers Published
 Kiselev, A; Tan, C, Finite time blow up in the hyperbolic Boussinesq system,
Advances in Mathematics, vol. 325
(February, 2018),
pp. 3455 [doi] [abs]
 Choi, K; Hou, TY; Kiselev, A; Luo, G; Sverak, V; Yao, Y, On the FiniteTime Blowup of a OneDimensional Model for the ThreeDimensional Axisymmetric Euler Equations,
Communications on Pure & Applied Mathematics, vol. 70 no. 11
(November, 2017),
pp. 22182243 [doi]
 Kiselev, A; Yao, Y; Zlatoš, A, Local Regularity for the Modified SQG Patch Equation,
Communications on Pure & Applied Mathematics, vol. 70 no. 7
(July, 2017),
pp. 12531315 [doi]
 Kiselev, A; Ryzhik, L; Yao, Y; Zlatoš, A, Finite time singularity for the modified SQG patch equation,
Annals of Mathematics, vol. 184 no. 3
(November, 2016),
pp. 909948 [doi]
 Kiselev, A; Xu, X, Suppression of Chemotactic Explosion by Mixing,
Archive for Rational Mechanics and Analysis, vol. 222 no. 2
(November, 2016),
pp. 10771112 [doi]
 Popov, IY; Kurasov, PA; Naboko, SN; Kiselev, AA; Ryzhkov, AE; Yafyasov, AM; Miroshnichenko, GP; Karpeshina, YE; Kruglov, VI; Pankratova, TF; Popov, AI, A distinguished mathematical physicist Boris S. Pavlov
(October, 2016),
pp. 782788 [doi]
 Kiselev, A; Zlatoš, A, Blow up for the 2D Euler equation on some bounded domains,
Journal of Differential Equations, vol. 259 no. 7
(October, 2015),
pp. 34903494 [doi]
 Choi, K; Kiselev, A; Yao, Y, Finite Time Blow Up for a 1D Model of 2D Boussinesq System,
Communications in Mathematical Physics, vol. 334 no. 3
(March, 2015),
pp. 16671679 [doi]
 Kiselev, A; Šverák, V, Small scale creation for solutions of the incompressible twodimensional Euler equation,
Annals of Mathematics
(November, 2014),
pp. 12051220 [doi]
 Iyer, G; Kiselev, A; Xu, X, Lower bounds on the mix norm of passive scalars advected by incompressible enstrophyconstrained flows,
Nonlinearity, vol. 27 no. 5
(May, 2014),
pp. 973985 [doi]
 Dabkowski, M; Kiselev, A; Silvestre, L; Vicol, V, Global wellposedness of slightly supercritical active scalar equations,
Analysis and PDE, vol. 7 no. 1
(2014),
pp. 4372 [doi]
 Kiselev, A; Nazarov, F, A simple energy pump for the surface quasigeostrophic equation,
Nonlinear Partial Differential Equations: The Abel Symposium 2010
(December, 2012),
pp. 175179 [doi] [abs]
 Kiselev, A; Ryzhik, L, Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case,
Journal of Mathematical Physics, vol. 53 no. 11
(November, 2012),
pp. 115609115609 [doi]
 Dabkowski, M; Kiselev, A; Vicol, V, Global wellposedness for a slightly supercritical surface quasigeostrophic equation,
Nonlinearity, vol. 25 no. 5
(May, 2012),
pp. 15251535 [doi]
 Kiselev, A; Ryzhik, L, Biomixing by Chemotaxis and Enhancement of Biological Reactions,
Communications in Partial Differential Equations, vol. 37 no. 2
(February, 2012),
pp. 298318 [doi]
 Kiselev, A, Nonlocal maximum principles for active scalars,
Advances in Mathematics, vol. 227 no. 5
(August, 2011),
pp. 18061826 [doi]
 Kiselev, A; Nazarov, F, Variation on a theme of caffarelli and vasseur,
Journal of Mathematical Sciences, vol. 166 no. 1
(April, 2010),
pp. 3139 [doi]
 Kiselev, A; Nazarov, F, Global regularity for the critical dispersive dissipative surface quasigeostrophic equation,
Nonlinearity, vol. 23 no. 3
(March, 2010),
pp. 549554 [doi]
 Berestycki, H; Kiselev, A; Novikov, A; Ryzhik, L, The explosion problem in a flow,
Journal d'Analyse Mathématique, vol. 110 no. 1
(January, 2010),
pp. 3165 [doi]
 Kiselev, A, Regularity and Blow up for Active Scalars,
Mathematical Modelling of Natural Phenomena (MMNP), vol. 5 no. 4
(2010),
pp. 225255 [doi]
 Kim, A; Kiselev, A, Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials,
Mathematical News / Mathematische Nachrichten, vol. 282 no. 4
(April, 2009),
pp. 552568 [doi]
 Kiselev, A, Diffusion and Mixing in Fluid Flow: A Review,
NEW TRENDS IN MATHEMATICAL PHYSICS
(2009),
pp. 357369, ISBN 9789048128099 [doi]
 Kiselev, A, Some recent results on the critical surface quasigeostrophic equation: A review,
HYPERBOLIC PROBLEMS: THEORY, NUMERICS AND APPLICATIONS, PART 1, vol. 67
(2009),
pp. 105122, ISBN 9780821847299
 Constantin, P; Kiselev, A; Ryzhik, L; Zlatoš, A, Diffusion and mixing in fluid flow,
Annals of Mathematics, vol. 168 no. 2
(September, 2008),
pp. 643674 [doi]
 Kiselev, A; Nazarov, F; Shterenberg, R, Blow up and regularity for fractal Burgers equation,
Dynamics of Partial Differential Equations (DPDE), vol. 5 no. 3
(2008),
pp. 211240 [doi] [abs]
 Kiselev, A; Shterenberg, R; Zlatos, A, Relaxation enhancement by timeperiodic flows,
Indiana University Mathematics Journal, vol. 57 no. 5
(2008),
pp. 21372152 [doi]
 Kiselev, A; Nazarov, F; Volberg, A, Global wellposedness for the critical 2D dissipative quasigeostrophic equation,
Inventiones mathematicae, vol. 167 no. 3
(January, 2007),
pp. 445453 [doi]
 Kiselev, A; Zlatoš, A, Quenching of combustion by shear flows,
Duke Mathematical Journal, vol. 132 no. 1
(March, 2006),
pp. 4972 [doi]
 Fannjiang, A; Kiselev, A; Ryzhik, L, Quenching of reaction by cellular flows,
Geometric And Functional Analysis, vol. 16 no. 1
(February, 2006),
pp. 4069 [doi]
 Andrzejewski, D; Butzlaff, E; Kiselev, A; Markely, LRA, Enhancement of combustion by drift in a coupled reactiondiffusion model,
Communications in Mathematical Sciences, vol. 4 no. 1
(2006),
pp. 213225 [doi]
 Berestycki, H; Hamel, F; Kiselev, A; Ryzhik, L, Quenching and Propagation in KPP ReactionDiffusion Equations with a Heat Loss,
Archive for Rational Mechanics and Analysis, vol. 178 no. 1
(October, 2005),
pp. 5780 [doi]
 Kiselev, A; Zlatoš, A, On discrete models of the Euler equation,
International Mathematics Research Notices no. 38
(August, 2005),
pp. 23152339
 Kiselev, A, Imbedded singular continuous spectrum for Schrödinger operators,
The Journal of the American Mathematical Society, vol. 18 no. 3
(July, 2005),
pp. 571603 [doi]
 Germinet, F; Kiselev, A; Tcheremchantsev, S, Transfer matrices and transport for Schrödinger operators,
Annales de l'Institut Fourier, vol. 54 no. 3
(2004),
pp. 787830 [doi]
 Constantin, P; Kiselev, A; Ryzhik, L, Fronts in reactive convection: Bounds, stability, and instability,
Communications on Pure & Applied Mathematics, vol. 56 no. 12
(December, 2003),
pp. 17811803 [doi]
 Vladimirova, N; Constantin, P; Kiselev, A; Ruchayskiy, O; Ryzhik, L, Flame enhancement and quenching in fluid flows,
Combustion Theory & Modelling, vol. 7 no. 3
(September, 2003),
pp. 487508 [doi]
 Christ, M; Kiselev, A, Absolutely continuous spectrum of Stark operators,
Arkiv för Matematik, vol. 41 no. 1
(April, 2003),
pp. 133 [doi]
 Kiselev, A; Last, Y; Simon, B, Stability of singular spectral types under decaying perturbations,
Journal of Functional Analysis, vol. 198 no. 1
(February, 2003),
pp. 127 [doi]
 Killip, R; Kiselev, A; Last, Y, Dynamical upper bounds on wavepacket spreading,
American Journal of Mathematics, vol. 125 no. 5
(2003),
pp. 11651198 [doi]
 Christ, M; Kiselev, A, Scattering and Wave Operators for OneDimensional Schr�dinger Operators with Slowly Decaying Nonsmooth Potentials,
Geometric And Functional Analysis, vol. 12 no. 6
(December, 2002),
pp. 11741234 [doi]
 Gesztesy, F; Kiselev, A; Makarov, KA, Uniqueness Results for MatrixValued Schrödinger, Jacobi, and DiracType Operators,
Mathematical News / Mathematische Nachrichten, vol. 239240 no. 1
(June, 2002),
pp. 103145 [doi]
 Constantin, P; Kiselev, A; Ryzhik, L, Quenching of flames by fluid advection,
Communications on Pure & Applied Mathematics, vol. 54 no. 11
(November, 2001),
pp. 13201342 [doi]
 Kiselev, A; Ryzhik, L, An upper bound for the bulk burning rate for systems,
Nonlinearity, vol. 14 no. 5
(September, 2001),
pp. 12971310 [doi]
 Kiselev, A; Ryzhik, L, Enhancement of the traveling front speeds in reactiondiffusion equations with advection,
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 18 no. 3
(May, 2001),
pp. 309358 [doi]
 Christ, M; Kiselev, A, WKB and Spectral Analysis¶of OneDimensional Schrödinger Operators¶with Slowly Varying Potentials,
Communications in Mathematical Physics, vol. 218 no. 2
(April, 2001),
pp. 245262 [doi]
 Christ, M; Kiselev, A, WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for OneDimensional Schrödinger Operators with Slowly Decaying Potentials,
Journal of Functional Analysis, vol. 179 no. 2
(February, 2001),
pp. 426447 [doi]
 Christ, M; Kiselev, A, Maximal Functions Associated to Filtrations,
Journal of Functional Analysis, vol. 179 no. 2
(February, 2001),
pp. 409425 [doi]
 Kiselev, A, Absolutely continuous spectrum of perturbed stark operators,
Transactions of the American Mathematical Society, vol. 352 no. 1
(December, 2000),
pp. 243256 [abs]
 Constantin, P; Kiselev, A; Oberman, A; Ryzhik, L, Bulk Burning Rate in¶Passive–Reactive Diffusion,
Archive for Rational Mechanics and Analysis, vol. 154 no. 1
(August, 2000),
pp. 5391 [doi]
 Last, Y; Kiselev, A, Solutions, spectrum, and dynamics for Schr�dinger operators on infinite domains,
Duke Mathematical Journal, vol. 102 no. 1
(March, 2000),
pp. 125150 [doi]
 Kiselev, A, An interpolation theorem related to the A.E. convergence of integral operators,
Proceedings of the American Mathematical Society, vol. 127 no. 6
(December, 1999),
pp. 17811785 [abs]
 Kiselev, A; Remling, C; Simon, B, Effective Perturbation Methods for OneDimensional Schrödinger Operators,
Journal of Differential Equations, vol. 151 no. 2
(January, 1999),
pp. 290312 [doi]
 Christ, M; Kiselev, A, Absolutely continuous spectrum for onedimensional Schrödinger operators with slowly decaying potentials: Some optimal results,
The Journal of the American Mathematical Society, vol. 11 no. 4
(October, 1998),
pp. 771797
 Kiselev, A, and a.e. convergence of integral operators,
Duke Mathematical Journal, vol. 94 no. 3
(September, 1998),
pp. 619646 [doi]
 Kiselev, A; Last, Y; Simon, B, Modified Prüfer and EFGP Transforms and the Spectral Analysis of OneDimensional Schrödinger Operators,
Communications in Mathematical Physics, vol. 194 no. 1
(May, 1998),
pp. 145 [doi]
 Kiselev, A, Some Examples in OneDimensional “Geometric” Scattering on Manifolds,
Journal of Mathematical Analysis and Applications, vol. 212 no. 1
(August, 1997),
pp. 263280 [doi]
 Christ, M; Kiselev, A; Remling, C, The absolutely continuous spectrum of onedimensional Schrödinger operators with decaying potentials,
Mathematical Research Letters, vol. 4 no. 5
(1997),
pp. 719723 [doi]
 Kiselev, A, Absolutely continuous spectrum of onedimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials,
Communications in Mathematical Physics, vol. 179 no. 2
(August, 1996),
pp. 377399 [doi]
 Kiselev, AA; Popov, IY, Indefinite metric and scattering by a domain with a small hole,
Matematicheskie Zametki / Mathematical Notes, vol. 58 no. 6
(December, 1995),
pp. 12761285 [doi]
 Kiselev, A; Simon, B, Rank One Perturbations with Infinitesimal Coupling,
Journal of Functional Analysis, vol. 130 no. 2
(June, 1995),
pp. 345356 [doi]


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Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

