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Alexander A. Kiselev

William T. Laprade Distinguished Professor of Mathematics
Mathematics

Research Interests


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

Selected Grants


Small Scale and Singularity Formation in Fluids

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2026

RTG: Training Tomorrow's Workforce in Analysis and Applications

Inst. Training Prgm or CMEPrincipal Investigator · Awarded by National Science Foundation · 2021 - 2026

Small Scale and Singularity Formation in Fluids

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2023

Small Scale and Singularity Formation in Fluid Mechanics and Biology

ResearchPrincipal Investigator · Awarded by Simons Foundation · 2020 - 2022

Regularity, blow up and mixing in fluids

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2018 - 2022

Fellowships, Gifts, and Supported Research


Topics in Applied PDE · July 2014 - June 2018 NSF The proposal focuses on three directions: intense structures in fluid flows, mixing by fluid flows, and effects of chemical attraction in biology, ecology and medicine. Fluid flows exhibit high degree of complexity and can easily develop intense structures. Better fundamental understanding of the mechanisms of creation of intense features in fluid flows is very important for many applications in engineering, weather forecasting and other fields. The first direction of the proposal seeks to study classical equations of fluid mechanics focussing on situations where intense fluid motion can develop spontaneously. Recent novel results obtained by the PI in this direction provide hopes for an essential advance in understanding these complex and important phenomena. In the second direction, a study of most efficient ways of mixing in fluid flow is proposed. Efficient mixing is of critical importance in many applications, ranging from combustion in engines to ecology. In the third direction, the PI will study the role of chemical sensing and chemical attraction for enhancement of reactions in biology. One situation where it is relevant involves healing of the body, where infected or injured tissues releases special compounds which attract immune system cells to fight the infection. Chemical attraction can also be an undesirable effect: some tumors are known to rely on this mechanism for their growth. The PI plans to develop new mathematical tools to analyze these more advanced and better predictive models. The project involves a training component, where junior researchers at all levels will be mentored as scholars and educators and will work on research projects under the guidance of the PI.
Regularity, Blow UP, and Mixing in Fluids · July 2017 - June 2020 NSF Fluids are all around us, and we can witness the complexity and subtleness of their properties in everyday life, in ubiquitous technology, and in dramatic weather phenomena. Although there is an enormous wealth of knowledge accumulated in the broad area of fluid mechanics, many of the most fundamental and important questions remain poorly understood. Of particular interest is the question whether solutions to equations describing fluid motion can spontaneously form singularities - meaning that some quantity becomes infinite. Understanding singularities is important because they often correspond to dramatic, highly intense fluid motion, can indicate the range of applicability of the model, and are very difficult to resolve computationally. More generally, one can ask a related and broader question of creation of small scales in fluids - coherent structures that vary sharply in space and time, and contribute to phenomena such as turbulence. The project aims to analyze singularity formation process for some key equations of fluid mechanics, and to better understand the mechanisms that generate small scales in fluid motion. Another direction of the project research focuses on mixing in fluid flow. Mixing in fluids plays an important role in a wide range of settings, from marine ecology to internal combustion engines. Here the goal is to find and study fluid flows that are especially efficient mixers, as well as to produce bounds on mixing efficiency given some natural constraints. Such bounds can serve as benchmarks in evaluation of mixing processes.
Simons Fellowship · July 2020 - August 2022 Simons Foundation · $130,000.00 Funding to supplement sabbatical leave of absence.
Small scale and singularity formation in fluids · July 2020 - June 2023 NSF · $430,000.00 Individual grant.
Training Tomorrow's Workforce · July 2021 - June 2026 NSF · $2,383,000.00 Training grant to support junior scientists and training activities on all levels: undergraduate, graduate, and postdoctoral.

External Relationships


  • Lake Como School of Advanced Studies
  • Max Planck Institute for Mathemtics in the Sciences, Leipzig
  • National University of Singapore
  • New York University, Abu Dhabi
  • Seoul National University
  • Lake Como School of Advanced Studies
  • Max Planck Institute for Mathemtics in the Sciences, Leipzig
  • National University of Singapore
  • New York University, Abu Dhabi
  • Seoul National University
  • UNIST, Ulsan, South Korea

This faculty member (or a member of their immediate family) has reported outside activities with the companies, institutions, or organizations listed above. This information is available to institutional leadership and, when appropriate, management plans are in place to address potential conflicts of interest.