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., et al. “Finite time singularity for the modified SQG patch equation.” Annals of Mathematics, vol. 184, no. 3, Jan. 2016, pp. 909–48. Scopus, doi:10.4007/annals.2016.184.3.7. Full Text

Kiselev, A., and A. Zlatoš. “Blow up for the 2D Euler equation on some bounded domains.” Journal of Differential Equations, vol. 259, no. 7, Jan. 2015, pp. 3490–94. Scopus, doi:10.1016/j.jde.2015.04.027. Full Text

Iyer, G., et al. “Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows.” Nonlinearity, vol. 27, no. 5, Jan. 2014, pp. 973–85. Scopus, doi:10.1088/0951-7715/27/5/973. Full Text

Choi, K., et al. “Finite Time Blow Up for a 1D Model of 2D Boussinesq System.” Communications in Mathematical Physics, vol. 334, no. 3, Jan. 2014, pp. 1667–79. Scopus, doi:10.1007/s00220-014-2146-2. Full Text

Kiselev, A., and V. Šverák. “Small scale creation for solutions of the incompressible two-dimensional Euler equation.” Annals of Mathematics, vol. 180, no. 3, Jan. 2014, pp. 1205–20. Scopus, doi:10.4007/annals.2014.180.3.9. Full Text

Dabkowski, M., et al. “Global well-posedness of slightly supercritical active scalar equations.” Analysis and Pde, vol. 7, no. 1, Jan. 2014, pp. 43–72. Scopus, doi:10.2140/apde.2014.7.43. Full Text

Kiselev, A., and F. Nazarov. “A simple energy pump for the surface quasi-geostrophic equation.” Nonlinear Partial Differential Equations: The Abel Symposium 2010, Dec. 2012, pp. 175–79. Scopus, doi:10.1007/978-3-642-25361-4_9. Full Text

Kiselev, A., and L. Ryzhik. “Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case.” Journal of Mathematical Physics, vol. 53, no. 11, Nov. 2012. Scopus, doi:10.1063/1.4742858. Full Text

Dabkowski, M., et al. “Global well-posedness for a slightly supercritical surface quasi-geostrophic equation.” Nonlinearity, vol. 25, no. 5, May 2012, pp. 1525–35. Scopus, doi:10.1088/0951-7715/25/5/1525. Full Text

Kiselev, A., and L. Ryzhik. “Biomixing by Chemotaxis and Enhancement of Biological Reactions.” Communications in Partial Differential Equations, vol. 37, no. 2, Feb. 2012, pp. 298–318. Scopus, doi:10.1080/03605302.2011.589879. Full Text