511 citations · 1.7k across the 69 of their papers we have counts for
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On Cayley Identity for Self-Adjoint Operators in Hilbert Spaces
Alexander V. Kiselev, Serguei Naboko
We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singula…
A simple energy pump for the surface quasi-geostrophic equation
Alexander Kiselev, Fedor Nazarov
We consider the question of growth of high order Sobolev norms of solutions of the conservative surface quasi-geostrophic equation. We show that if is large then for every gi…
Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
Michael Dabkowski, Alexander Kiselev, Vlad Vicol
We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velo…
Biomixing by chemotaxis and enhancement of biological reactions
Alexander Kiselev, Lenya Ryzhik
Many processes in biology involve both reactions and chemotaxis. However, to the best of our knowledge, the question of interaction between chemotaxis and reactions has not yet bee…