Alexander A. Kiselev

Alexander A. Kiselev
  • William T. Laprade Distinguished Professor of Mathematics
  • Professor of Mathematics

Research Areas and Keywords


Fourier analysis, functional analysis

Biological Modeling

Chemotaxis, enhancement of biological reactions

Mathematical Physics

Spectral theory, Schrodinger operators

PDE & Dynamical Systems

Fluid mechanics, Euler equation, surface quasi-geostrophic equation, singularity formation, small scale creation, mixing efficiency

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. 

Education & Training
  • Ph.D., California Institute of Technology 1997

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. “Nonlocal maximum principles for active scalars.” Advances in Mathematics, vol. 227, no. 5, Aug. 2011, pp. 1806–26. Scopus, doi:10.1016/j.aim.2011.03.019. Full Text

Kiselev, A., and F. Nazarov. “Variation on a theme of caffarelli and vasseur.” Journal of Mathematical Sciences, vol. 166, no. 1, Mar. 2010, pp. 31–39. Scopus, doi:10.1007/s10958-010-9842-z. Full Text

Kiselev, A., and F. Nazarov. “Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation.” Nonlinearity, vol. 23, no. 3, Feb. 2010, pp. 549–54. Scopus, doi:10.1088/0951-7715/23/3/006. Full Text

Kiselev, A. “Regularity and blow up for active scalars.” Mathematical Modelling of Natural Phenomena, vol. 5, no. 4, Jan. 2010, pp. 225–55. Scopus, doi:10.1051/mmnp/20105410. Full Text

Berestycki, H., et al. “The explosion problem in a flow.” Journal D’Analyse Mathematique, vol. 110, no. 1, Jan. 2010, pp. 31–65. Scopus, doi:10.1007/s11854-010-0002-7. Full Text

Kim, A., and A. Kiselev. “Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials.” Mathematische Nachrichten, vol. 282, no. 4, Apr. 2009, pp. 552–68. Scopus, doi:10.1002/mana.200810754. Full Text

Kiselev, A., et al. “Relaxation enhancement by time-periodic flows.” Indiana University Mathematics Journal, vol. 57, no. 5, Dec. 2008, pp. 2137–52. Scopus, doi:10.1512/iumj.2008.57.3349. Full Text

Constantin, P., et al. “Diusion and mixing in fluid flow.” Annals of Mathematics, vol. 168, no. 2, Dec. 2008, pp. 643–74. Scopus, doi:10.4007/annals.2008.168.643. Full Text

Kiselev, A., et al. “Blow up and regularity for fractal burgers equation.” Dynamics of Partial Differential Equations, vol. 5, no. 3, Jan. 2008, pp. 211–40. Scopus, doi:10.4310/DPDE.2008.v5.n3.a2. Full Text

Kiselev, A., et al. “Global well-posedness for the critical 2D dissipative quasi-geostrophic equation.” Inventiones Mathematicae, vol. 167, no. 3, Mar. 2007, pp. 445–53. Scopus, doi:10.1007/s00222-006-0020-3. Full Text