511 citations · 1.7k across the 69 of their papers we have counts for
45 papers · 1 filter
Suppression of chemotactic singularity by buoyancy
Zhongtian Hu, Alexander Kiselev, Yao Yao
Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of f…
Small scale formation for the 2D Boussinesq equation
Alexander Kiselev, Jaemin Park, Yao Yao
We study the 2D incompressible Boussinesq equation without thermal diffusion, and aim to construct rigorous examples of small scale formations as time goes to infinity. In the visc…
On nonexistence of splash singularities for the -SQG patches
Alexander Kiselev, Xiaoyutao Luo
In this paper, we consider patch solutions to the -SQG equation and derive new criteria for the absence of splash singularity where different patches or parts of the same patch…
Stirring Speeds Up Chemical Reaction
Siming He, Alexander Kiselev
We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, the interplay between chemical diffusion a…
Chemotactic Reaction Enhancement in One Dimension
Yishu Gong, Alexander Kiselev
Chemotaxis, the directional locomotion of cells towards a source of a chemical gradient, is an integral part of many biological processes - for example, bacteria motion, single-cel…
Small scale formations in the incompressible porous media equation
Alexander Kiselev, Yao Yao
We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an app…
The Flow of Polynomial Roots Under Differentiation
Alexander Kiselev, Changhui Tan
The question about the behavior of gaps between zeros of polynomials under differentiation is classical and goes back to Marcel Riesz. In this paper, we analyze a nonlocal nonlinea…
Boundary layer models of the Hou-Luo scenario
Siming He, Alexander Kiselev
Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou \cite{HouLuo14} proposed a new fi…
Chemotaxis and Reactions in Biology
Alexander Kiselev, Fedor Nazarov, Lenya Ryzhik +1
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions. One example is the immune syste…
Functional model for boundary-value problems
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the…
Small scale creation for solutions of the SQG equation
Siming He, Alexander Kiselev
We construct examples of solutions to the conservative surface quasi-geostrophic (SQG) equation that must either exhibit infinite in time growth of derivatives or blow up in finite…
Analysis of a Singular Boussinesq Model
Alexander Kiselev, Hang Yang
Recently, a new singularity formation scenario for the 3D axi-symmetric Euler equation and the 2D inviscid Boussinesq system has been proposed by Hu and Luo based on extensive nume…
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev
A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotic…
Global Regularity and Fast Small Scale Formation for Euler Patch Equation in a Smooth Domain
Alexander Kiselev, Chao Li
It is well known that the Euler vortex patch in will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solution…
Global regularity for 1D Eulerian dynamics with singular interaction forces
Alexander Kiselev, Changhui Tan
The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion…
Global regularity for the fractional Euler alignment system
Tam Do, Alexander Kiselev, Lenya Ryzhik +1
We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the se…
Finite time blow up in the hyperbolic Boussinesq system
Alexander Kiselev, Changhui Tan
In recent work of Luo and Hou, a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the…
Stability of Blow Up for a 1D model of Axisymmetric 3D Euler Equation
Tam Do, Alexander Kiselev, Xiaoqian Xu
The question of the global regularity vs finite time blow up in solutions of the 3D incompressible Euler equation is a major open problem of modern applied analysis. In this paper,…
Finite time singularity formation for the modified SQG patch equation
Alexander Kiselev, Lenya Ryzhik, Yao Yao +1
It is well known that the incompressible Euler equations in two dimensions have globally regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart…
Local regularity for the modified SQG patch equation
Alexander Kiselev, Yao Yao, Andrej Zlatos
We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified SQG equations. These involve a parameter which appears in th…
Suppression of chemotactic explosion by mixing
Alexander Kiselev, Xiaoqian Xu
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many instances, processes involving chemical attraction take place in fluids. One of the most s…
On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations
Kyudong Choi, Thomas Y. Hou, Alexander Kiselev +3
In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we…
Blow up for the 2D Euler Equation on Some Bounded Domains
Alexander Kiselev, Andrej Zlatos
We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of it…
Finite time blow up for a 1D model of 2D Boussinesq system
Kyudong Choi, Alexander Kiselev, Yao Yao
The 2D conservative Boussinesq system describes inviscid, incompressible, buoyant fluid flow in gravity field. The possibility of finite time blow up for solutions of this system i…