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math.AP2018
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…
math.AP2018★ 30 cited
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…
math.AP2018
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…