5 citations · 5 across the 3 of their papers we have counts for
4 papers
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…
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…
Global regularity of two-dimensional flocking hydrodynamics
Siming He, Eitan Tadmor
We study the systems of Euler equations which arise from agent-based dynamics driven by velocity \emph{alignment}. It is known that smooth solutions of such systems must flock, nam…
Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flow
Siming He
In this paper, we use the distance comparison principle, first been developed by G. Huisken, to study the spatial curve shortening flow. We have got the result that if the initial…